 Either you want to ask a question and you will ask your question yourself, but you just want to, you know, I'm gonna put everybody in a certain, not an order, but I'm gonna have a list of who's gonna ask, and I'm gonna ask you to ask your question yourself. You can send me a message for that, but you can also send me a message with your question itself, and I'll ask it on your behalf to the speakers if you want some anonymity, because you want to ask a question that you think I don't know. You want some anonymity, okay? You can send me a message and I'll ask the speakers the question for you, okay? But please do so, and even if you stole me, you want to ask a question, just send me a message. It's easier that way, and I have a list, and I can just name you and you can ask a question, or I will ask a question myself, okay? And is everybody gonna be here? Who's gonna be here for speakers? We've got a couple of speakers that are gonna be here. But mainly, I think, like you said, questions can be general about pretty much anything. Welcome back. I hope everybody had a good lunch. So let me continue. And this is something I feel much more comfortable, because I'm speaking about reality. And in general, I'm talking about three categories of compounds. It's materialization of quantum spin liquid. One is the organic triangular system. And the second one, I would like to discuss about Kagome lattice quantum spin liquid. And at the end, I would like to discuss about the type of quantum spin liquid on Hanikama lattice. But before speaking about reality, let me give you a few comments on how to identify quantum spin liquid experimentally. So somehow, we are looking for state of nothingness. Something I get the question, why are you looking for such a boring state? Nothing there. Okay. But I think the first thing experiment that does access is measurement of magnetic susceptibility. Okay. And if you do see famous curious behavior at high temperature, that is kind of evidence for low tide moment. And in general, if you have magnet ordering, you are supposed to see kink in magnetic susceptibility. Okay. So that's kind of an undergraduate class. But this is often called the QD plot. So plot of one over chi, you know, versus temperature. Okay. And you can find this even in Kitte textbook. You know, if you plot one over chi versus temperature. Okay. Normally, anti pheromagnet, you see kind of linear behavior. And expect to QD-wise temperature. Exemplation closes, you know, at minus QD-wise temperature. Okay. And this is some sort of near field transition temperature. And also a very good measure of interaction. Of course, if you know, you have, you know, coincidence of pheromagnetic and anti pheromagnetic interaction within the same system, you know, often, you know, those QD-wise temperature is, you know, kind of a difference between those two and doesn't, you know, give you a good measure of, you know, near field transition temperature. But otherwise, you know, this is very good measure of, you know, interaction. And this ratio, you know, mean field transition temperature versus real transition temperature, near temperature is often called, you know, a frustration parameter. So that characterizes the degree of frustration. And then, you know, mean field like classical anti pheromagnet, you know, they do show magnetic ordering, you know, evidenced, you know, by this, you know, kinky here. Okay. And the ratio of QD-wise temperature and near temperature is over the order of one. This is a boring mean field magnet. Okay. But if you go anti, frustrated anti pheromagnet, like a triangle like this, you know, magnet. Okay. So, because, you know, torsion is suppressed to lower temperature. So therefore, the ratio between QD-wise, you know, versus, you know, near temperature is more than one. So typically, you know, we often find the ratio of 10, you know, even kind of 1000 in frustrated magnet. So this frustration parameter often shows up in the literature. Okay. Now, you know, if, you know, you find that, you know, no ordering like this, you know, if, you know, you miss, you know, this kind of kinky magnetic susceptibility. Now, you have a big chance of, you know, discovering, you know, quantum spin naked. In terms of frustration parameter, if you don't see any kick, frustration parameter is kind of infinite. It depends on degree of disorder. And the small disorder, we don't care. But the big disorder, you know, it kind of smeared out. And often, if that is the case, we see kind of grassy behavior. And the grassy behavior means that if you measure sustainability on cooling or warming, you see some hysteresis. And that's kind of a, you know, grassy behavior is also a signature of freezing of spring moment, but in a random way. But, you know, like, sometimes, you know, as, you know, there was a question about that, you know, in the kind of presence of strong frustration, fluctuation due to dimensionality disorder, often, you know, those kink susceptibility is kind of smeared out, as you pointed out. That's a very good question. And heat capacity, okay, if, you know, fluctuation is, you know, around, you know, it again is kind of smeared out. So, in that sense, you know, specific heat, you know, are easily to measure. They are not, you know, so sensitive, you know, to long range ordering if, you know, fluctuation is kind of significant. And maybe, you know, you can go neutron scattering or X-ray magnetic scattering. However, it's easy to say, oh, there is, you know, magnetic peak. Okay? But it's not that easy. It's kind of negative proof. So, oh, there is no magnetic peak. Okay? And often, actually, in order to see, you know, kind of absence of any kind of ordering, many experienced go either enamel or muon spin rotation. They are quite sensitive to internal field. And even, you know, if, you know, the ordering is like a glacier, you know, there is a distribution of magnetic field, internal magnetic field. And you can see those, you know, glassy freezing as, you know, brooding of peak. Okay? So, they are kind of often used to prove for, you know, absence of magnetic ordering. Okay? And you'll see that in a minute. Okay? And once you establish the absence of, you know, ordering, you are highly likely, you know, you know, discover the, you know, quantum spin liquid. Then, you know, you might, you know, characterize, you know, elementary excitation. Right? Of course, observing continuum is a direct evidence of fractional rotation. So, you may want to go, you know, Neutron eniastic scattering to characterize, you know, continuum. But on the other hand, you know, you have to be careful. Neutron colleagues are quite greedy. And they often require like cubic CC, you know, big, you know, crystal. But if you find a new compound, it's not, you know, that easy to get cubic, you know, CC crystal. And so, if, you know, you have difficulty to go Neutron eniastic scattering, but still, you can sense elementary excitation. For example, you know, from, you know, susceptibility. If it is kind of a gap pool, you know, you see exponential supplation of susceptibility, reflecting gap. But if you have a gap-less spin liquid, normally, you know, susceptibility, go to a finite value, at t equals zero limit. And from that, somehow, you can tell whether, you know, your spin liquid is kind of a gap pool or a gap-less or the same is true for specific heat. And if you have kind of a gap-less spin liquid, like if you have spin on Fermi's surface, right? So you see t-linear specific heat, like, you know, metal. Metal, because of presence of, you know, finite, you know, density of state of electrons, you see t-linear specific heat. And in some of, you know, quantum spin liquid candidate, you see t-linear specific heat, like, just like a metal, though they are insular. And also, nowadays, you know, measuring thermal conductivity is, you know, quite fashionable. As you noticed, you know, from the talk by Yuji Matsuda last week. Since, you know, spin doesn't carry any charge, right? So you cannot use a current meter to measure, you know, property of your quantum spin liquid. But of course, spin can carry entropy, and it turns out that, you know, thermal conductivity is very good to, you know, pull off to measure, you know, spin excitation. And in particular, you know, specific heat, you know, measures only entropy. So they don't care whether your spin excitation is localized or eternal. But, you know, thermal conductivity, you have to create a heat flow. That means, you know, if, you know, your excitation detected by thermal conductivity, okay? That means, you know, your excitation is kind of mobile. Okay? So that's kind of an important point. Okay? But anyway, so using the technique, you know, somehow in the last, you know, almost, you know, 10 years, experimenters, you know, discovered many, you know, realistic quantum spin liquid, you know, candidate. Okay? And this is kind of a table, you know, Leone balance called it, you know, eight years ago. But yeah, since then, we have, you know, a couple of compounds, okay, discovered. On top of that, you know, we have, you know, recentry image type, you know, compounds. So now, you know, we have plenty of examples. Okay? And among them, let me speak about first, RBB type, you know, quantum spin liquid in organics, which is supposed to be the cleanest quantum spin liquid. Then, okay, this one along. Let me speak about, you know, in organic, you know, Kagome lattice compound called the hybrid, you know, smith side. Okay? And then, you know, finally, I would like to discuss, you know, quantum spin liquid. So let me begin with organic system as, you know, cleanest example of quantum spin liquid. And I'm going to speak about those zero two compound. Okay? So I have to confess. I don't know how to read it. I was horrible in chemistry class. And I don't understand the organic chemistry. Okay? But what I know is that, you know, they are like a ionic crystal. And so, like a sodium chloride. And so, that's why they are called charge transfer salt. Okay? So, you know, the molecule is kind of neutral. But charge is kind of transferred. Electrons are kind of transferred from yellow molecule to white molecule. Okay? So, like this BEDT TTF system. Okay? So, you have kind of stack of, you know, BEDT molecule layer and some acceptor layer, you know, colored in white. And donor layer, acceptor layer. And the charge is kind of electron kind of transferred from yellow to white. Okay? And normally, you know, the molecule has, you know, even number of electrons. Right? But by transferring one charge, you know, they have, you know, odd number of electrons. And because those kind of molecules, you know, are kind of highly kind of localized. And as a result, you know, they are, you know, multi-insulator. So, here is, you know, real space in the picture of those, you know, yellow molecule in real space. And as you see from two, actually, you know, you have a pair of molecule called a dimer. Okay? And those, you know, pair of dimer share one electron or to be put one hole. Okay? By transferring charge to acceptor layer. Okay? And those kind of electrons are kind of highly kind of localized and form, you know, electron crystal, multi-insulating state. Okay? And as you see, you know, in the real space, they align like this. And that, you know, by, you know, calculating a contaminant chemistry, you must know, you know, main source of interaction with, you know, neighbor is like this. And there are kind of two type of interaction. Okay? One is, you know, called T. And the other is, you know, T-ply. Okay? So, like this. So, therefore, if, you know, T and the T-ply is kind of comparable. Okay? And now, you know, magnetic interaction between spin one-half, you know, moment kind of an equal on the triangular lattice. And this could be a greater, you know, flagrant for, you know, geometrical frustration. Okay? Two-dimensional S equal one-half triangular moment. Okay? And in fact, for, okay, and the, you know, the basic structure is the same for this palladium demittinum compound. Okay? And this compound, okay? By changing anion, you know, you know, chitonous layer, okay? You can control, you know, kind of lattice constant. And you can change, you know, ratio between T and T-ply. Okay? And as I said, you know, when T equal to T-prime, you know, you have a perfect, you know, triangular geometry. Okay? And as you see, there are a number of compounds with different, you know, you know, acceptor layer. And if, you know, T-ply is, you know, much smaller than T, like 0.7, 0.8, okay? As you see, okay, this, this means anti-ferromagnetic transition. So, the frustration is not strong enough. Okay? They do experience anti-ferromagnetic order. Like coming close to T-ply-mico-1, okay? Somehow, this, you know, mean feel like transition is kind of suppressed gradually by increasing, you know, frustration. And eventually, you know, around, you know, 0.1, 0.9, 90 percent, okay, those structural phase transition kind of disappeared. Okay? And this is a specific compound. They say it's located, you know, around here. Okay? So, it's not, you know, perfectly, you know, one-to-one-to-one ratio, you know, triangle. But they have one-to-one-to-point-to-nine ratio triangle. But still, they do see quantum spin-legged state. And how do I know the grand state of those, you know, organic components, quantum spin-legged? Okay. So, here is, you know, plot of NMO signal. Okay? So, somehow, each, you know, correspond to magnetic field, your kind of nuclear fields. This case, a carbon nuclear field. Okay? And so, like, if you have magnetic ordering, you know, they're going to produce, you know, internal magnetic field. And normally, anti-ferromagnetic, you know, you have a different magnetic field. So, therefore, peak springs. Or if you do have a glassy environment, you know, like, spin freezes in a glassy manner, you have, you know, distribution of a magnetic field, you know, from, you know, side to side. So, you do see a broadening of peak. Okay? And this, you know, compound, okay? This compound, T is not equal to T prime. I think, like, over the point, you know, seven. Okay? And on cooling, okay, another 25 point K, you see sprit of peak. Okay? And this circuit represents magnetic ordering. So, they created the internal kind of magnetic field. And as a result, the peak in the sprit. Okay? This is very clear signature of magnetic order. But if you make, you know, compound, almost, you know, T prime equal to T, you know, ideal triangular situation, okay? Down to 30 millimeter, you know, you don't see anything. So, that's kind of a signature of massive, state of nothing. And the same compound, the different compound, you know, paradigm compound, okay, you don't see anything. Down to 20 millimeter. Yes. Okay, there is that kind of study. Yeah. And so, they do study some sort of a quantum critical point. And in particular, organic is extremely soft, right? So, even a small amount of pressure, you can change lattice constant a lot. So, that's kind of big advantage of organics. Okay. So, okay, those compound, you know, you know, we do see kind of the state of nothing. That's why they go, this should be quantum spin. As I said, you know, this whole mark of quantum spin liquid, it kind of fractionalization. And if, you know, we have, you know, a way like ground state, it's equal to one excitation split into two spin and a half, you know, excitation called spinon. And that's kind of very unique. And they could form some sort of a Fermi surface of spinon, like, you know, one day, right? And can I detect, you know, fractionalization in quantum spin liquid? So, let me give you first textbook explanation of free electrons. And if you take a look at Tito textbook, there is a discussion on free electrons. And you have, you know, Pauli susceptibility from, you know, conduction electron. And that is scaled by density of states. Okay. And there is a T linear specific heat. People often call it gamma. Okay. That is, again, scaled by density of states. And those kind of thrift are the kind of constant, like a Boltzmann constant. Right? Therefore, if you have, you know, free electron, the ratio of, you know, Pauli susceptibility in magnetic susceptibility. And specific heat, you know, T linear constant gamma should be constant. Okay. And in metal, we often, you know, take a ratio of chi and gamma and call it, you know, Wilson ratio. And if we have free electron metal, this ratio, okay, normalized by this constant should be one. But in reality, if you have a kind of free molecule and the interaction, this factor, you know, they will, can, they will form one, but normally it's over the order of one. So, observing Wilson ratio close to one is a very good signature of having a free molecule. So, this is for free electrons. And if you have, you know, Fermi surface spin, in essence, yeah, we should have, we can have, you know, quite a similar phenomenon, because spinon has spin, right? So, they can, yeah, to magnetic field, like free electrons. And they have entropy. The difference is, you know, those quantum spin liquid is uninsulated. However, we have, you know, chi-neutral excitation called spinons. And they behave like, you know, free electron, right? And they can, can we see something like that, okay? So, here's the picture, okay? So, okay, this is susceptibility. At high temperature, you know, you, you can see curie-like behavior, you know, it's actually going to increase, you know what I mean? And the, the, there's a kind of glow peak, and it eventually goes down, and the susceptibility approaches, you know, finite value, okay? Over the order of 3 to the 10 to the minus 4, okay? So, there seems to be a finite susceptibility, okay? And again, you know, let me emphasize no kink observed, okay, consistent with the absence of any magnetic ordering, okay? And the susceptibility approaches a finite value, means, you know, we seem to have some sort of finite, you know, densitric excitation and the spin-liquid kind of gapless, okay? And the major specific heat, or semi-compound, okay? This is, you know, C over T versus T square plot, you know, kind of a classical way of plotting specific heat at low temperature. And the extrapolation to T called zero, okay, give you gamma values, T over T values, you know, this is a standard analysis for metal, okay? And, you know, those, you know, compound, okay, you know, T plan, it's not equal to T, and they do show magnetic ordering. And the magnetically ordered, you know, compound, you know, this specific heat, C over T, go to zero, that means no finite gamma value, or no density of states. But those, you know, colored compound is kind of spin-liquid compound, then you see they exerted finite value around 10 millijoule per mole square, okay? So, somehow, both susceptibility and a specific heat show to, you know, we have kind of finite density of states, yes. Yeah, actually, some people, some theorists have discussed that, but we didn't see any kind of oscillation at all there. Yeah, there's a discussion like that, yeah. Yes. Could you speak loudly? Yeah, yeah, yeah. So, there's a kind of clear signature of magnetic ordering here. Yeah, yeah. So, this is kind of a reference, yeah. But I'm talking about this compound, and this is the kind of susceptibility I'm talking about, okay? So, how do you like susceptibility? And if I take ratio, actually, somehow, you know, the ratio is almost one. Amazing, right? It's insulator, no electron running, but ratio is kind of close to one, and a finite liquid. So, we have no adjustable parameter, but the ratio is just, you know, close to one. So, like maybe, yeah, yeah, some, if you are kind of experimentalist, if you could remember, okay, like a 10 to the minus 4 in the susceptibility, it's roughly 10 millijoule in terms of gamma, if it was on ratio one, okay? So, take a look at 10 to the minus 4 in the 10, you immediately see, you know, yeah. You know, in terms of real-time ratio, the contribution is kind of consistent with each other, okay? This is kind of another compound, you know, I showed. And again, you know, you see, in fact, out of two, you know, in fact, out of two larger, you know, you know, kai zero, you know, t equals zero value, but again, it would be 10 to the minus 4. But, you know, gamma is also kind of enhanced by fact out of two. So, therefore, the ratio again close to one. So, although we don't have any free electrons in the system, but clearly, there is some excitation which satisfies the, you know, recent ratio, go one. So, yeah, this could be a very strong signature of, we have some sort of Fermi surface of spinon in those compounds. And even bigger supply that brought, you know, by Yuji Matsuda, he was a speaker last week. And he measured thermal conductivity of, you know, the semi-none compound. And if you take a look at Hitler's textbook, okay, thermal conductivity is scaled by specific heat and the velocity, the velocity is kind of a, you know, slope of dispersion and the mean free path, okay? So, kind of thermal conductivity essentially pull off the specific heat. However, they have to carry heat. So, there is a factor mean free path, okay? And if, you know, your excitation is kind of localized, okay, mean free path zero, okay? So, therefore, you don't detect your excitation in thermal conductivity channel, okay? And so, they brought the quantity kappa divided by T, okay? So, C divided T is nothing but gamma, right? So, gamma times mean free path, okay? And here is, you know, quantum spin degree compound. And you see finite intercept. And we more or less know velocity, okay, from, you know, energy scale of interaction. And we know what is gamma, you know, okay, from here. So, we can estimate, you know, what is L? And Yuji kind of estimated L should be at larger one micron. So, this fluctuate like, like excitation can trouble really over one micron. Amazing, right? So, that's why they start discussing, you know, whether, you know, can we have some sort of a magnetic field is active. But this means, you know, our excitation is kind of a highly mobile. And we have kind of Fermi surface, you know, which satisfies, you know, recent ratio. And they are kind of highly mobile. Oh, in that sense, yeah, you know, I believe this, you know, organic triangular magnet is kind of a best example, yeah. Yeah, so I think it's roughly one nanometer. Yeah, like oxide is 0.3, 0.4. And, yeah, not one or another magnitude, but, you know, factor of 2, 3. Also, actually, yeah, another way to take a look at that is, like, if you measure kind of a metal, okay, you are supposed to have, you know, finite T linear term in thermal conductivity due to finite gamma term. And this contribution, 0.2, is not, you know, as large as like copper. But if you bring dirty metal, like, you know, brass, you know, brass. Brass, actually, at Roteba Schwarz, you know, quite similar magnitude of T linear term. So, like, this, you know, quantum magnet is insulator. However, as you know, thermally conducting as, you know, brass, okay. So something, you know, must be telling it, right? That's great, isn't it, right? So in this sense, I think at moment, this represents, you know, kind of physics of spin on, you know, in a nice manner. Of course, there are many issues kind of left, you know, even in organic, you know, spin leakage. For example, so I showed you kind of two compounds, okay, and this compound we saw, you know, highly mobile kind of, you know, excitations, okay. And at Roteba, this is, you know, measurement of, you know, NMO 1 over T1, relaxation rate, okay. So this kind of reflects some sort of density of spin excitations. And somehow, in the temperature dependence around 1K, you see some clear anomaly. And at the moment, you know, people don't understand what they did, okay. So I showed there below 1K, and that to nicely follow, you know, this Wilson ratio equal 1, but above that, you know, we see some anomaly there. And at the moment, they don't know what they did. And some of, you know, romantic theorists discusses that this could be a fake transition of a spin-on-fame surface, like that. But still, you know, we don't understand what they did. Other issue is kind of, yeah, this actually, I can link my lecture to Andrei. Somehow, all those kind of organic compounds, right next to those quantum spin liquid, you always find superconductivity. Some people discuss those quantum spin liquid physics might have something to do with superconductivity. But on the other hand, you know, some compound with, you know, T-pline, you know, much more so than T, and therefore, shows you, you know, long-range ordering under pressure. They show superconductivity, as well. In that sense, you know, you find superconductivity not only when you have quantum spin liquid in the state, but also, you know, even when you have, you know, magnetically ordered state, you find superconductivity. Yes. This, this, this fake, yeah, this is, this is a weak, very weak, you know, fast order. So, there is some critical point, you know, more critical point, you know, here. And above that, you see kind of close-over. That's what this, and some people discussed, you know, kind of critical point, you know, here in terms of more criticality. That's actually not, not many are known. Yeah. But however, you know, you know, those quantum spin liquid, you know, material, there are, you know, three major states, you know, known so far. One is magnetically ordered. Second one is quantum spin liquid. Third one is so-called, you know, charge ordered. So, you have kind of one electron per side, but this electron moved to the next side, and the former, you know, very strong, you know, I shouldn't say dimer, but you have kind of two electron, zero electron, two electron, zero electron, that kind of charge order state. And I'm not sure, actually, this specific case, you know, represents the charge order of the case, but I suspect this could be charge order state. Any questions so far? Yeah. Yeah. Yeah. Of course, there are, you know, many theories. Of course, this, you know, the story of RWB actually started, you know, from that. So, in that sense, there are kind of many stories to connect RWB type spin liquid and superconductivity. And Yonbak gave a bit specific case, but in general, people discuss that. But on the other hand, I don't know any experiment evidence which does support, you know, real liquid, you know, quantum spin liquid and superconductivity. As I told you, like this phase could be magnetically ordered state, but still, you know, I find superconductivity. Okay? Of course, you can take, you know, this, you know, in a different way. Okay? But the question, if you Google QSL, you know, superconductivity, you'll find the many theoretical papers on that. So, if you're interested, yeah. Yes. So, let me give you a second example. Okay? Now, you know, moving out, you know, from Triangle, let me speak about Kagome Rades. And Kagome Rades is, in some sense, you know, particularly interesting because of the confusion among, you know, big, you know, theorists. Okay? I haven't collected all the paper, but, you know, still there is a kind of big debate among you know, theorists, whether, you know, Kagome Heisenberg anti-ferromagnet should be, you know, gap-less U1 quantum spin liquid or, you know, G2 gap-tune spin liquid. Okay? Maybe, you know, the easiest way is to do the experiment. Right? And, you know, and some time ago, those, you know, chemistry colleagues learned, you know, kind of a mineral called the hybrid smithite. Okay? So, this compound has been known from mineral, you know, so geophysics knows that this, you know, for long. And somehow, they created, you know, the compound, cleaner compound in the lab. Okay? And the structure of this compound is kind of interesting. So, essentially, you know, their structure is, you know, pyrichloral lattice, three-dimensional pyrichloral lattice, like pyrichlorilidate. Okay? But as I said, you know, if you take a look at pyrichloral lattice along, you know, one, one, one direction, you have, you know, stacking of triangular layer and Kagome layer. And in this compound, Kagome layer is kind of fully occupied, you know, cup two plus, s equal one half. And the triangular layer is supposed to be occupied by non-magnetic D10 zinc plus, zinc two plus. Okay? But somehow, you know, nature doesn't allow completely clean, you know, triangular layer. And we know, you know, some zinc, you know, invade the territory of zinc. Okay? So, there is some chemical disorder there. But anyway, so, as a first approximation, in this compound called high-bathsme site, you have, you know, Kagome lattice of a cup of two plus. Now, following, you know, recipe, you know, I told you at the beginning. So, here's the kind of plot of, you know, 1 over chi plus 10. And this 1 over chi extrapolates something like, you know, minus, you know, 200, to be precise, minus 180k. So, somehow, average scale of magnetic interaction is anti-ferromagnetic over the order of 180k. Okay? Well, you don't see anything. Okay? Down to T-co zero. No knocking, you know, anything. Okay? So, yeah, in this sense, you know, fluorescence parameter is kind of infinite, you know, in this compound. And they check, you know, like magnetic scattering in the USO and no signature. And this is going to end there now. And it's a bit complicated because, you know, a copper occupies a different chemical site. But you don't see any kind of broadening. You see kind of some broadening, but no real splitting down to low temperature. So, they say, you know, grand state, you know, should be quantum spin naked. But compared with organic, you know, we have to admit, you know, that in organic, you see kind of some broadening. And, you know, environment is not as clean as, you know, organic compound. But since big, you know, crystal for high-versive site is kind of available. And, yeah, Jonson and Lee at Stanford, they did the Newton in elastic scattering measurement. Okay, so this is kind of a K-vector, one-one-zero direction. This is the energy. And this green means you see, you know, kind of finite excitation. And as you see, you know, Maglon dispersion is not, you know, well defined. But instead, you have quite a broad, you know, continuum here. And they say, you know, we observed some sort of, you know, spinon continuum in Newton scattering. And this could be evidence of fractional excitation. Okay. That's why people believe this could be quantum spin naked. As I said, you know, theoretically, you know, there is kind of confusion, whether there is a kind of small gap in spin excitation or not. That, you know, recently, you know, though people try to see kind of some gap in NMO channel. Okay. So this is kind of night shift, you know, susceptibility as a function of temperature. This is kind of an expansion. And somehow at, you know, low field, okay, it's a bit complicated. But somehow, susceptibility seems to die out exponentially like this. And from this, you know, they claimed, you know, oh, yeah, at low field, there should be spring gap. Okay. And by applying a field, somehow this exponential decay is kind of, you know, fade out. And instead of, you know, somehow, you know, they try to, you know, decay, you know, much more slowly. They did some sitting and extracted, you know, kind of, you know, excitation energy out of this, you know, from three points, you know, they are kind of brave enough. And the protein excitation, you know, energy, excitation temperature as a function of magnetic field. And they say, you know, extrapolation of zero field, they get, you know, a gap of 10 Kelvin. And with applying field, somehow, gap is kind of surplus and the dissipate around 10 Tesla. But remember, remember, so, you know, what one Tesla, in terms of, you know, Kelvin, what is, you know, one Tesla, 0.56 Kelvin, right? So, like 10 Tesla is roughly 10 K, right? So, if you have some sort of a secret gap and apply 10 Tesla, you know, 10 Tesla, you can surplus, you know, gap. And somehow, you know, that's kind of consistent. So, from that, you know, they claimed, you know, they would have some sort of singlet like, you know, gap in zero field. That could be surplus by applying magnetic field. And if, you know, their interpretation is kind of correct, okay? G2 gap of spin liquid is kind of correct, okay? But somehow, because of this, you know, big error, but, you know, the dissipation is kind of still ongoing. You can see how, you know, we can take a look at all kind of data, right? So, yeah, somehow, like I told you, you know, I always state that you don't have, you know, exact solution. And, you know, maybe I can say, you know, that's why it is interesting, you know. But on the other hand, you know, we cannot do kind of fine kind of argument based on kind of theoretical, you know, attempt. And recently, you know, you can have quantum spin liquid in the show that that's why, you know, everybody went to that direction so far. And as I said, you know, in this morning, we have a spin one-half moment on top of Hanikamura, this, okay? And there is a kind of, you know, conflict of bond between X bond, Y bond, G bond. And by introducing two kind of mylarna, you know, you can have, you know, kind of exact, you know, grand state. So, you don't have to rely on that kind of numerics. And you support to see two kind of elemental excitation, reflecting, you know, fractionalization. One is, you know, low-lide mylarna and, you know, called G2 flux, okay? The other is kind of Eiterant Mylarna, okay? And of course, you know, suddenly, you know, Phyllis of Mylarna showed up and, you know, like, you know, community wanted to materialize it. You know, in general, spin one-half, pure spin one-half moment, you know, J form is just, you know, high level anti-fail magnet. Because, you know, you need kind of spewed coupling and anisotropy, right? To realize the Ising spin one-half. And somehow, you know, around the same period, you know, kind of, you know, physics of, you know, strong spewed coupling system. And it is in four-plus oxide, imaged. And somehow, though two-flow, like a breakthrough in quantum magnetism, and kind of new, you know, arena in correlated electron physics, you know, namely, you know, heavy transcemental oxide, married, and created the interesting playground for the exploration of steve spin naked. So the point is, you know, she's a pure spin one-half, you know, in general, you know, they are coupled, you know, in Heisenberg, right? So instead of spin one-half, you know, let's try to use, you know, some sort of a spin one-half, like, but the spin of the entangled object, right? So you have, you know, kind of LS coupled J object in heavy transcemental element. And that kind of hidden degree of freedom, like orbital degree of freedom. And using that, you know, can we realize, you know, Ising spin one-half, you know, like, you know, system. So the point is, for one, I think as, you know, Yonbach emphasized yesterday. So those are, you know, 4 plus oxide, you have, you know, 5-E, you know, T2G electron, 5. And as you know, in the octahedral coordination, like peribus kite, those, you know, 5-4 degenerate the T2 orbital, split into EG and T2G. But for 5D, you know, your wave function is quite big, okay? And that, you know, they win against, you know, funt coupling. And as a result, you have kind of low spin state, all 5-E electron accommodated into T2G orbital. Now this T2G orbital, you know, triplet degenerate can be treated as if, you know, they are P orbital, electrical one, but minus sign. The reason, actually, you know, Yonbach kind of explained yesterday. And somehow, we do not, you know, those, you know, heavy, so, transition metal element, like a region, speed of coupling is as large as half electron volt, okay? So they are kind of compatible to cool on you, you know, even kind of heavy energy, okay? And therefore, they do kind of split into J effective one half state, meaning, you know, orbital moment and the spin moment aren't parallel to each other. And J effective three half state, spin moment and orbital moment are parallel to each other, okay? And if you have five, you know, those three half, you know, it's kind of carpet, so they are completely filled. And you have, you know, one electron in J equal one half, you know, state, okay? And you have kind of one electron per orbital situation, you know, that's why, you know, most state is kind of relatively stable in this kind of compound, despite, you know, cool on you is quite modest over the order of one to two electron volt. Now, the beauty of this, you know, J one half moment, okay, in a pure J one half limit, if you calculate the G factor, G factor two and plus minus one half, so they are just like spin one half. But of course, you know, they are kind of a complex state made of orbital moment and spin moment. And this is kind of a wave function of J one half state. And then you have, you know, equal mixture of X, Y, Y, G, G, X. But the point is, you know, you have kind of ups here in X, you know, orbital, but the down spin here in Y, G, G, X, orbital, okay? So you have a mixture of up spin and down spin, okay? So therefore, those spin orientation is quite orbital dependent. And that is kind of a key to get a complicated interaction. And also, there is an imaginary index, you know, I here, that means, you know, orbital is kind of rotating. So it's kind of orbiting around the nucleus, okay? But, you know, in calculating the extension of process, this, you know, imaginary index, you know, plays a very important role, okay? So, and somehow, you know, my colleague, you know, George Jackery and Gignard Caglioli, they noticed that because of, you know, this complicated wave function, you know, the coupling between two J one moment is, you know, very much, you know, complicated. And when, you know, those original oxygen octahedron share edge like this, you know, they share edge, and you have two 90 degree bond. And if we consider only super exchange process, super exchange, okay, through oxygen, then you have kind of two oxygen between two J one moment, okay? And if you, you know, consider super exchange, you know, you know, among X, Y, Z, G, X, you know, specific orbital state is in charge of, you know, electron hopping, right? And they found, because of two oxygen here, and the imaginary index I, those, you know, super exchange parts, exchange hopping parts, interfere with each other. And the other, you know, conventional exchange, you know, coupling is zero because of interference. So, those two parts act as interferometer, and, you know, conventional anti-ferro exchange kind of zero, that's what they found. So, therefore, they find dominant, you know, process is, you know, dominant process is kind of fully occupied, the carted below one half to one half. So, electron kind of hopping, you know, from J three half to J one half. And once, you know, you transfer one electron from site one to site two, okay, you have kind of a full coupling between three half and one half. And that's kind of another key. And because of the coupling, you have a special specific contact axis, and the coupling is quite easy, okay? So, therefore, this is a spin one half like, okay? However, you know, because of this interference, you know, exchange is a bit, you know, complicated, and they have, you know, ferromagnetic interaction and quite, you know, icing, okay? So, to make, you know, a long story in short, you know, because of, you know, a specific nature of this wave function, you know, the super exchange interaction is very isotropic. Only when two spins happen together to this original oxygen plane, you know, there is ferromagnetic interaction, but otherwise interaction zero. So, here actually we have a very important ingredient of a Kitech model. Icing, you know, fellow equivalent to spin half. Now, so nature is kind of great. We didn't create intentionally. It already exists. And this compound was studied, you know, from battery people as a candidate for lithium battery, okay? So, my lawyer just told, you know, George Jackley, or there is a Hancom compound made of, you know, lithium and Elysium. And this compound, Elysium-2, Elysium-3, and as I told you, in this morning, this structure can be derived from sodium chloride. So, you can make triangular lattice, you remember, by inserting Elysium. And by replacing, you know, one out of three Elysium with non-magnetic Elysium, you can create a Hancom lattice. So, this is it, right? Now, so, you can see network of octahedral like this, Hancom lattice. And as you see, J-shell edge, right? So, you have 90-degree bond, interferometer. So, this should, you know, give rise to using a ferromagnetic interaction. And if, you know, I take a look at, you know, one specific, you know, Elysium-Oxygen octahedral, okay? They are connected to three neighbors because of Hancom lattice. And there are three orthogonal edges, okay, in octahedral, okay? So, somehow, three bond as, you know, three orthogonal edge planes, okay? So, therefore, this plane gives you X, you know, Elysium, you know, ferro. This gives you Y, Elysium, ferro. This gives you G, Elysium, ferro, right? So, if, you know, we have only spike change, okay? This gives you ideal materialization of Kitech model. But of course, super exchange is not the only exchange path. It cannot be quite a big issue to moderate quantum spin liquid. But of course, but, you know, at this point, you know, my point is somehow nature is great. They don't know anything about Kitech, but somehow those compounds capture essential ingredients of Kitech model, okay? That's kind of excitement. And somehow, you know, everybody rushed into those, you know, compounds. But as you see, you know, QD-wise plot, okay? First of all, QD-wise, you know, temperature is something like minus 100. That means anti-ferromagnetic. But I discussed the ferromagnetic is an interaction. But like QD-wise tells you, anti-ferromagnetic. Here you already see something unfavorable comes into this problem. Next, you know, if you do see susceptibility, you can see clear King here and there. So that means there is, you know, anti-ferromagnetic ordering. And in fact, you know, as you know, many, you know, speaker emphasize this compound made of sodium shows the zigzag, you know, anti-ferromagnetic ordering. And this compound shows spiral magnetic order. We kind of created the three-dimensional analog of this compound. Okay? So what we, yeah, so this compound we accidentally found and the name to, you know, hyper-hanicam. Okay? So this is kind of a two-dimensional hand camera. Okay? And hand camera, you can view as, you know, like this zigzag chain connected by bridging, you know, bond, like your red, zigzag chain. And you rotate this, you know, zigzag chain up and connect to next layer. Okay? But still all, you know, iridium cycle kind of equivalent. And that's 320-degree bond. So this is nothing but, you know, three-dimensional analog of hand camera. And many theorists including Yonbak Kim, you know, checked in the grand state of, you know, hyper-hanicam lattice. And they showed, you know, kind of same, you know, quantum spin liquid with myelanoferemium could be grand state. But nevertheless, those compounds, unfortunately, we find, you know, long-range kind of order of state. And the Newtonian chloride showed up new generation of, you know, hand camera compound. Again, you know, they have kind of same, you know, structure features, you know, hand camera lattice of, you know, octahedral, edge-shared. They do show long-range ordering at 13 Kelvin. But nevertheless, you know, people try to check, you know, high-energy excitation. And they saw kind of some signature of continuum excitation in this compound. And they say, you know, this could be a kind of high-energy signature of, you know, quitaifium continuum. And also, they applied magnetic field parallel to hand camera layer and found those zigzag anti-ferromagnetic order disappeared. And somehow, system damage, you know, paramagnetic down to low temperature. And this could be, you know, spin-liquid-like phase. And, you know, Yuji Matsuda found quantized, you know, thermal fall effect in this, you know, critical region. So, you know, we don't see, you know, real quantum spin-liquid state. But somehow, you know, we have shared, you know, our system is very close to quitaifium quantum spin-liquid. I think the timing is kind of up. So, and yeah. So, that's kind of last year, two messages I want to deliver you. It's a most recent progress. And one is, you know, by, you know, my colleagues. And, you know, you just, you know, modify compound by replacing a lithium in between with, you know, proton hydrogen. And just, just, it's kind of black magic. You know, somehow, by replacing a lithium with hydrogen, somehow the signature of long-range order is gone. Okay. And NML, you know, you see the state of nothing down to 1K. So, this is the same Hancom compound, but doesn't show any sort of long-range ordering down to below 1K. So, somehow on Hancom lattice, we found the quantum spin-liquid state. But somehow, we checked, you know, low-lying citation and, you know, below 10K, somehow, specifically dominated by lattice. And we don't see any kind of magnetic contribution. But as I said, you know, we are supposed to see, you know, ordering of G2 flux at low temperature around 1K if it is a pure type. Right. So, in the sense that we found the, you know, quantum spin-liquid, but somehow it doesn't follow, you know, kind of prediction for pure type system. And somehow additional ingredient seems to be playing some role. And at the moment, we don't know what kind of quantum spin-liquid it is. And the second recent, you know, progress is, you know, coming from Yuji Matsuda. And this plutonium chloride system, as I said, you know, by applying field, you can suppress long-range ordering. And the only thing I'm kind of worrying about is here, actually, you know, if you take a look at the magnetic data, because you apply field as large as 910 Tesla. Okay. So you have, you know, big, you know, in this moment of 0.6, 0.7 muV. Okay. In that sense, you know, a certain fraction of entropy kind of lost. Still, you know, Yuji Matsuda observed, you know, quantization of whole effect. Okay. Half, you know, quantization state. And that is kind of predicted for Mylana-Kaila edge state. And that's kind of a hot topic. So my conclusion for this architect part is somehow, yeah, reality comes in. And in many components, I observed long-range ordering. But some new progress, you know, came up very recently. And we have some sort of a quantum spin liquid. We don't know what it is, but on hand cameras. And we see some signature of topological Kaila edge state in kind of resin chloride. In the sense, we are kind of about there. Okay. So long story, in short, I started, you know, talking about many exotic phases of correlated electrons. And I emphasize the, you know, kind of phase combination between them. And the quantum spin liquid state is my favorite. Okay. And I believe a fascinating state of elective matter, you know, it's fit to my mind of, you know, the state of nothingness. And if you could feel kind of rapid, you know, progress in materialization, I'm kind of more than happy about it. And as you see, this field, kind of an intimate collaboration between theory and the experiment quite important. Okay. So, you know, experiments have to handle with kind of disorder and so on. And we have to handle with kind of chemistry. But on the other hand, you know, theorists, you know, those are kind of too complicated. And they have to rely on kind of finite size numerics. And somehow we have to compensate each other intimately. And in the sense that this is kind of an interesting field where, you know, theory and the experiment can collaborate very seriously, intimately. Okay. So if you, you can kind of join us, I would be more than happy about it. So thank you very much for your attention.