 Okay. So good morning everybody. So let me first identify who I am. So I am a kind of material physicist and I have been looking for new compound with exotic you know state. In particular you know those you know formed by so-called correlated electrons have been kind of my field for a long. So I like you know are on yesterday you know I attended to you know one of the very first high TC conference in Toureste in 1988. So that means I'm old again and since then you know I have been motivated to look for kind of exotic phases you know from materials you know perspective. Okay. So today among you know many exotic you know phases you know let me speak about the quantum spin liquid. Yeah. So let me speak about the quantum spin liquid. And during two weeks you know there are many talks on quantum spin liquid and I'm gonna give you a bit lower level of you know lecture than you know those you know given kind of earlier. And yesterday and the day before yesterday you on back you know gave a nicer intuitive picture you know using analogy with you know BCS superconductor and quantum spin liquid. And that you know last week Natasha gave a beautiful overview of quantum spin liquid. And the UG Matsuda you know gave you know some sort of state of art discovery of you know cantites you know thermal hole effect. And today you know I try to cover a bit you know bigger kind of perspective of quantum spin liquid in general. Not only quantum spin liquid but so called the RVV type you know quantum spin liquid. So here is kind of outline. And I have you know two lectures in the morning one in the morning and you know the other in the afternoon. And then in the morning let me try to give you kind of a concept you know background. Okay I'm going to give you you know kind of experiment as the way of you know what is you know quantum spin liquid. And first you know I'm going to discuss about you know kind of a classical canonical quantum spin liquid based on RVV. And then you know let me give you an experimental way of understanding you know what is you know Kitev quantum spin liquid. In the afternoon let me take you to the world of reality. Meaning that you know we have you know number of you know compounds where you know those you know quantum spin liquid is highly likely realized. And let me you know show you some of you know convincing example of quantum spin liquid in the old material. Okay starting from organic you know quantum spin liquid to inorganic you know quantum spin liquid and the later Kitev you know quantum spin liquid. And let me show you you know how to take a look at all the experimental data. Okay so this might be a bit too naive but you know when you know we learned you know solid state you know physics we learned you know the out test you know orbital in solid determines you know electric you know property. And the each you know orbital can accommodate you know two electrons you know up and down spin. And if you have you know two electrons you know the orbital are completely occupied and the material is kind of bond insulator. But if you have you know only one electron power without you know using a bacon site you know they kind of travel around almost freely and therefore some sort of electron gas. Okay and that's a kind of very basics of Kondesmar. But in so called that torrential metal oxide which you know I have been working for you know more than kind of 30 years. The out test orbital is the orbital. And if you take a look at the wave function of you know any called three orbital state as you can see you know the you know radial distribution of wave function becomes narrower and narrower on going from 3F to 3D. And 3D you know the orbital is quite localized so they are kind of orbiting you know very hard. Okay and because that you know 3D orbital tend to be kind of confined in space substantially. And if you put two electrons on the same orbital you know we estimate you know Coulomb deposition between two electrons could be 2 to 10 electron volt. Actually if you naively calculate Coulomb deposition between two electrons you know with you know one almost long distance you will get something like 10 electron volt. Okay so this 2 to 10 electron volt kind of quite natural number. And then this Coulomb new is even larger than you know a typical Fermi energy two electron volt. And as a result the motion of you know electron is you know kind of blocked by you know Coulomb repulsion. If you know electron want to hop you know next you know site. If you know other electron sitting already you know you will be pushed back. Okay and as a result in order to hop around the electron has to find the vacant site. And because that you know electrons are kind of strongly entangled that's why we call those you know electron system correlated electrons. So this you know correlated electron you know if you know they move around can be viewed as you know electron like it. And in the limit of you know strongly you know Coulomb new you know finally you know electron you know stop you know moving around and form some sort of a solid called the motto insulator. And as you see you know charge degree of freedom is completely blocked but of course you have a spin degree of freedom up and down and using this you know the system could be a magnet. And you know through those kind of interaction inside the solid okay you can have you know variety of electric phases you know formed. Not only electron gas but sometimes you know correlated the liquid sometimes electron solid like electron crystal super fluid could be viewed as superconductor. And we discuss liquid crystal state of you know electrons. And those are kind of my target you know what do you know I call electric models in solid. And of course you know you know each electron has you know charge minus e and you know they have you know choice of spin up and down. And also the orbital is in general five four degenerate okay. So you have a choice of you know which orbital you should choose okay. So that you know we call multiple degrees of freedom. And often you know those you know charge spin orbital degree of freedom behave independently from each other. For example you know you can have a situation like charge solid you know charge doesn't move but the spin remains in the liquid state called the spin liquid which I'm going to speak about. Although not yet identified people discuss you know possibility of orbital liquid okay. So charge is kind of solid however you know orbital kind of fluctuating. That kind of state could exist. Now of course in reality you know charge spin orbital you know they are not completely independent with the other and they kind of coupled you know because they belong to the same electron. And the form even more complicated set of organized pattern of charge and spin orbital okay. That's why you know those you know phases of you know electrons are kind of interesting. And a typical example of electric phase you know you might be able to find it in high Tc cuprate. So as many of you know you know mother compound of high Tc cuprate it's you know D9 you know 4-1 mother insulator. And that situation you can view as you know electrons. Electrons from it. And as they are insulators and as they experience you know magnetic you know phase transition into anti afl magnet. And that situation you can view as you know spin liquid you know solid transition. And by doping you know soil melt into stranger you know liquid state. This might be viewed as electron liquid you know crystal called pseudo gap state. And eventually you know they became you know electron liquid where we have electron liquid. But on the way you have you know D-wave superconductivity. And of course in a dilute limit you know they should be viewed as simple electron gas. And in a you know transition metal oxide okay you can see those you know exotic active phases you know here and there. And here is kind of some of the example of you know phase diagram of transition metal oxide. And you can see many phases are competing with each other right. So you have solid one solid two liquid one liquid two you know kind of phase competition is one of the hallmarks of oxide physics. Now by recognizing those you know richness of electric phase in transition metal oxide let me focus you know one kind of specific charming phase kind of my favorite phase. And my favorite phase is you know quantum spinning which is you know title of today. So suppose you know we have you know charged solid multi insulator okay. So now you know because of a coolant power electron cannot move okay. And if you know neighboring spins are kind of anti-parallel each other as you know. Still you know this electron can hop to you know next you know site by costing coolant energy you. But in case of ferromagnetic arrangement you know because of probably exclusion principle you know this you know spin cannot travel to next site okay. So only when you have anti ferromagnetic you know configuration you can gain kind of some energy by you know perturbation something like this. So if you know you have you know single orbital multi-unit state in general you know magnetic interaction between two spins anti ferromagnetic okay. Of course if you have you know more than one orbital relevant you know the situation is much more complicated. But through this you know so-called exchange in the process you know you know most of you know multi-insulator is anti ferromagnetic. And then before you know this kind of high Tc cube plate you know our hero Phil Anderson you know wrote a you know one paper you know almost 50 years ago now. So he said that a new kind of insulator. So why he meant it's if you know you have you know anti ferromagnetic okay anti ferromagnetic multi insulator anti ferromagnetic coupled spins on top of a scalar at least you know you simply have up down up down configuration that's kind of quite you know stable. So this situation can be viewed as a spin solid. But if you put it on kind of triangle okay there are no way you know to find a you know configuration all the bond are kind of happy meaning in anti ferromagnetic. And with combination with you know counter effect counter fluctuation you know on the kind of triangle at least you know Anderson stated you know grand state is some sort of you know counter spin and this kind of he named you know a new kind of insulator 50 years ago. Okay so I don't know you know how to express the image of a quantum spin like it but it's kind of something like this. And then you know and I you know this kind of motivated experiment a lot and you know many experimenters even kind of one or two generation you know before me have been looking for quantum spin state based on triangular magnet. But somehow you know those attempt wasn't you know quite you know successful. And after high Tc somehow you know material committee community you know come come to counter you know magnetic community you know clobby and I think that was you know big you know breakthrough for the community. And now you know we have you know many kind of a candidate for in Anderson quantum spin. And I said that you know combination of a geometrical frustration and the counter fluctuation. And let me give you you know quite an experimental way of you know what it kind of counter fluctuation and instability of anti ferromagnetic. Okay so this is kind of anti ferromagnetic. So you have you know up and up down up down you know configuration and the pointing G direction that's kind of anti ferromagnetic. And you know start from you know Heisenberg you know anti ferromagnetic Hamiltonian. Okay so you have kind of three component XYG but this configuration you know they can gain only through G component. And then because that you know when you know they discovered anti ferromagnetic. As far as I understand there are discussion you know whether anti ferromagnetic you know could be stable or not. And why you know anti ferromagnetic kind of unstable you know let me use you know some sort of a hand waving argument. Consider only two spins okay neighboring two spins okay you know coupled you know Heisenberg. And as many of you know you have you know kind of four states up and down times two. And those state in the presence of Heisenberg interaction you know split into singlet gaining you know minus three-quarter J and the triplet you know gaining you know and that's kind of unstable you know quarter J you know above you know zero energy. Okay so the grand state is you know many of you know spin singlet and that is kind of superposition of up down and down up okay. And consider you know anti ferromagnetic situation just you know up down. And as you see you know this anti ferromagnetic situation is a superposition of 50% triplet and the 50% singlet. So this is you know configuration you know the energy is you know minus you know quarter J okay. So by kind of adding you know two different you know configuration he actually you gain kind of some energy okay you know coming from here. And so this you know sometimes as far as I understand the people call it anti ferromagnetic or anti ferromagnetic is not you know robust against the quantum fluctuation superposition of those two and the singlet is kind of stable. And I think that that's kind of a basis of Anderson's argument. Now once knowing that you know those you know singlet or quantum fluctuation you know stabilizes singlet you know state maybe you might you know consider what could be ground state okay. And the easiest is you know you place singlet you know pair you know regularly on top the ladders. So you form ladders of you know spin singlet pairs okay. And again you know the energy of spin singlet. And this situation is called variance bond solid. So it means that you know this spin singlet you know pair you know occupies a specific side you know they form ladders that's why we call it variance bond solid. We often write down like a VBS state okay. And apparently you know this state okay you are kind of breaking you know symmetry. And I often you know this state is not you know so stable if you do calculate it. But you forget about ladders. And in reality you know we often see those you know balance bond solid state in real material because you know you have coupling to ladders. And once you know you have kind of shortened bond by ladders distortion you can stabilize this singlet state and stabilize the balance bond solid state. So this state is you know not you know so unstable okay. But you know if you don't like you know lattice distortion maybe you know instead of having a solid state of you know singlet you may prefer you know kind of super portion of different you know distribution of spin singlet okay. So like on a triangular lattice because of geometric frustration you have you know many way of you know placing a spin singlet on top of triangular lattice okay. And let's consider you know constant super position of different distribution of you know singlet state. So the state is kind of yes. Balance bond in the solid fully gains this singlet and therefore spin singlet yeah yeah yeah. But compared with those you know if you do calculate numerically you know often those states are kind of more kind of stable. But in reality you know there are coupling with lattice and that could change you know thing. Anyway so and if you you know consider like a singlet you know pair you know on a neighboring you know lattice you know we call it you know short range you know resonating balance bond state. So this is kind of you know most naive image of what is you know quantum spin ligates okay. So you have you know kind of a short range you know singlet you know pair and you have you know many way to distribute the spin singlet on to triangular lattice and why don't we consider all kind of state and quantum mechanically you know sum out okay. So those states are kind of a quantum mechanically kind of you know fluctuating. But because of super position okay what's important is they do not you know break symmetry. So symmetry not you know block okay. And at the moment you know we consider only next nearest you know nearest neighbor singlet pair and that we call the short range algorithm. But of course you might you know consider you know long range you know singlet pair okay. Then actually you have you know even more kind of a different you know possible you know choices and you can consider you know super portion of you know long range you know pair. That is called the long range algorithm. And at this state okay you know perhaps you know those you know singlet are only nearest neighbor singlet. So in order to excite you know those kind of a singlet you have to create a triplet. So this you know state it's kind of highly likely you know you have a kind of gap in the excitation. However those long range in RVB it's kind of super position of a strong pair and the moderately you know slog in a pair very weak pair and eventually you know zero. So there is a kind of a distribution of excited state okay. So you can have you know zero energy excitation and then you have you know kind of a continuum excitation. Because the presence of you know strong pair and weak you know pair. And at this you know we expect you know excitation is kind of a gapless okay. But again you know by super posing all those different state global symmetry not you know block. But as you see you know from this so those two are called the quantum spin liquid. Okay because of a quantum super position of a singlet state. But you know as you see you know you can have you know many different you know kind of you know quantum spin liquid. So quantum spin liquid is not uniquely defined. I think this is kind of one of the most important in this morning. And one of the hallmarks of those you know quantum spin liquid state is called the fluxionization. In order to break up you know spinning a pair you have to create a spin triplet okay. S equal one kind of excitation. But in a quantum spin liquid you know those you know S equal one kind of excitation you know they can kind of split into two free S equal one half like excitation. And so this situation we have you know elementary excitation like a spin one half. This is called spinon. And this is kind of a pharaonic. And you know people believe you know they can form some sort of a pharynx surface of you know spinons okay. And since spin one excitation split into two spin and a half you know people call it fluxionization. So in a conventional magnet it's actually some people discussed last week you know you have you know well defined you know magnon dispersion. Line of excitation. But you know quantum spin liquid because of those mobile you know spin one half you know excitation called spinon okay. And even they can form a kind of pharynx surface. So the excitation is like a metal. And you can have you know kind of a continuum excitation. So people take you know the presence of a continuum excitation as kind of evidence for fluxionization okay. So this is actually you know you can find the finding her textbook yes. So this is just you know like a metal yes. Could you speak up please you know so actually there's air conditioning above me. Yeah so I think you know even in a you know short-range RVV case there could be kind of a spinon. I think that could be kind of quite an important distinction between you know kind of thinking so yeah. For example like Kagome lattice you know they could have gap but still you know they discuss language of continuum and fluxionization yeah yeah I think yeah I think so but there could be subspecies right yeah it should be yes. Oh that's a very good question maybe you know is there any neutron scatter in the audience. In general you know higher the process you know intensive much kind of weaker right yeah yeah yeah thank you. And of course you know this concept of fluxionization you know came from 1D system. So 1D Heisenberg we have kind of exact you know kind of you know solution you know based on the answer and you know by neutron deflection you can see beautiful kind of continuum you know like this and this actually you know people believe you know kind of experimental evidence for fluxionization of spin excitation in case of 1D. And this can be compared with you know kind of theory in a sophisticated way okay. So there is a kind of analogy between 1D or 2D or you know many of the concepts of 2D you know came from kind of 1D. But the the difference is following so in case of 1D we know what is exotic ground state as far as I understand. But in case of 2D you know this RVB like state including short length you know long length you know nobody obtained that you know RVB like you know state as exact solution of any Hamiltonian you know. So the only way to do kind of new medical you know calculation but new medical calculations you know they're kind of side effect and you know they're kind of a sign problem and you know they're kind of a you know confusion among theory quick. And I don't have a deep understanding of you know what is the kind of point. But like you know let me you know quote the example of you know spin one half you know Kagome anti ferromagnet okay. You know what the Kagome lattice right. And the Kagome lattice you know anti ferromagnet you know you have redefined Hamiltonian but nobody can solve it. And people that's you know kind of new medical calculation but there was kind of a you know big you know confusion among theorists okay what could be the grand state of Kagome anti ferromagnet until very recently and like somebody said you know okay so Kagome anti ferromagnet you know there should be a kind of small gap in spin excitation like a short range you know RVB and you know that should be described as kind of a G2 gap spin liquid but some people say oh this is gapless you want spin liquid and there are still kind of many paper archive okay. And I don't know who should kind of trust you know so I'm sorry but so let me say some people said oh this is kind of final answer but then you know another paper shows up no no it's not in final answer yet and there should be you know gap you know there should be gapless something like that and let me talk about this subject you know afterwards you know by showing some of our experimental realization of Kagome lattice okay. So in the sense you know RVB spin liquid I think everybody believe existence but somehow reality is kind of not fully understood yet you know compared with you know 1D that's kind of message and somehow you know maybe you you you can say you know two statement one is you know okay though I will be kind of spin liquid you know you know kind of theoretical support is not good enough okay or you know you may say because you know theory cannot you know predict what it is that's why it is interesting to the experiment you know there could be kind of two way of understanding current you know situation but anyway recognizing you know that kind of chaos there was a kind of big you know kind of recent breakthrough by Alex you know that's you know what I want to tell you next okay. So somehow you know Kitef is not you know in the Konnetsumata community but he suddenly jump into this you know issue you know from the perspective of you know quantum computation and so on and some time ago I think you know you know more than kind of 10 years ago he proposed that you know he's Hamiltonian called the Kitef Hamiltonian. There are many Hamiltonian with the name of Kitef but this is you know one of the most famous one Kitef model on hand camera days okay and somehow he kind of find this you know Hamiltonian you know you he can get the exact you know solution and now you know from his work you know actually what is you know quantum spin liquid exactly and that's why you know everybody's kind of motivated you know to work on the you know Kitef quantum spin liquid nowadays okay. So what you know Kitef did was he placed the spin one half you know moment on hand camera okay so in the sense that you know the model is quite simple you know when on hand camera and spin one half and now on hand camera you have you know three bonds right so called 120 degree bond right on the hand camera and as you see you know those kind of three bond are colored like a green blue red okay so actually you can color all kind of bond okay in three color on the hand camera days and he placed you know some sort of a strong you know icing ferromagnetic interaction on top of those kind of three bonds okay and this is an easy axis on the bond okay you have a choice and in his model okay okay this you know red little bond okay easy axis g direction and a blue bond icing axis y direction okay and a green bond easy axis is x direction okay so you have you know three orthogonal icing easy axis for three bond okay and they are orthogonal to each other I think that's the point so naive image is like I suppose that you have you know spins on top of number six right and if you consider bond within number one you know they want to polarize spin along g direction right but green you know they want to polarize you know spins along x direction and the blue try to polarize you know spin on six to y direction x y g orthogonal okay so three you know orthogonal pretty hard direction so therefore those you know three bond conflict with each other on number six right each side you know you have been conflict of three bond okay that gives a strong you know frustration like a triangle okay that that's the source and then naively you know like you can make a like a happy bond right you know like you know green would like to polarize spin along x right so you have you know spin x pere among pair on this you know green bond and the blue you know you can have you know spin why you know fellow bond okay and then they're kind of happy and those two you know they don't talk each other right so they can fill up in all kind of spins which kind of happy bond like this way and of course you know like you know triangle lattice there are many way of filling hand cam lattice which is only happy bond and you may consider you know super position of different you know arrangement of happy bond okay so each spin must choose you know one happy bond okay but you can distribute happy bond different way and then you can have you know super position of you know those in happy pair so this is come somehow to you know similar to our real estate and the innocence that you know I believe this model is kind of in deeper connected to you know our real estate okay but of course this is a kind of experimental way of understanding that but you know theorists are much senior smarter than me and you know actually exactly solved his Hamiltonian and let me trace what he did okay on my understanding okay if you know I say something wrong maybe you know you know correct me so this is kind of Hamiltonian and the first point is you can define a quantity called the g2 flag okay so you kind of a merge polite you know those kind of word you know spring operator along hexagon okay one two six okay so this is called the g2 flux in quantity and somehow you know it shows that this g2 flux commute with you know Hamiltonian okay so therefore you know w you know g2 flux is a concept property okay and that you know this is kind of local you know quantity okay so therefore you can define okay and that you know again value of w is kind of plus minus one so you have you know plus minus one flux for each kind of bracket because you know w is conserved in the local quantity and that's kind of as far as I understand that you know one of the first important point and then actually he introduced you know so-called the Magrana you know operator you know it's quite a mathematics like a full Milano operator you know x y g direction and you know matter you know Milano c and you replaced that you know spring operator with you know two Milano operator p and c so as Yonbak discussed yesterday so this Hamiltonian you know you have you know four Milano operator product of four Milano operator but there is a you know pattern coming from c and also from b like you know a but you know you can easily find even I can calculate that this b commutes you know h and also w so it kind of measures that you know this you know g2 flux and take you know plus minus you know one so if you know so that means you know consider you know this a you know this time kind of plus minus one okay so you have you know something like a j ci dagger cj that's you know nothing but you know Hamiltonian of electron on top of Hancock already so then she should have you know kind of a direct like you know dispersion okay that's why you know you you have you know direct like you know dispersion of you know matter my life and this p term defines this you know hopping in a parameter so if you know this you know flux is not in order you have kind of a random phase you know plus minus you know from you know placket to placket but at low temperature you know flux you know that order and then actually you have kind of uniform you know phase and then you have direct dispersion that's kind of grand mistake that's you know what you know how you know kitex of this Hamiltonian as far as you know I understand okay but now you know this w is kind of a local you know quantity okay and you know kind of conserved so like excitation related to w should have a gap okay and the real spin real spin is kind of a combination of b and c but it must you know contain you know b kind of operator so therefore in a you know excitation of a real spin you know you have to kind of excite you know this g2 flux so therefore you might expect a gap in kind of spin excitation but anyway so you know this seminar work of work tape we have you know exactly sort of quantum spin liquid you know finally we see what it is and grand state is kind of consist consisting of two kinds of marina fermions you know one is a dirac which is kind of a gapless and the other is kind of localized you know defined you know each you know hand come to hand come so called g2 flux that is the kind of gap but once you know that but I cannot but the theorists can calculate you know what kind of response you can expect you know from a type you know can come spinning and this is you know one of the you know earliest you know calculation you know by you know I honest know and my friend that you know relatively you know emotional and this is a dynamical structure so it's kind of a neutron scattering a spectrum okay and you see you know kind of continuum excitation okay and on top of that you see do you see kind of blue here okay this is kind of zero excitation okay so meaning there is a kind of a gap in the excitation and I understand that this small excitation gap you know comes from local g2 flux because you know spin operator you know of excited real spin you know you have to you know deal with two kinds of marina and you know one is a kind of localized marina and you know flipping you know plus minus one that's quite local in character and have a excitation gap so somehow you know at least that this is a direct dispersion of matter you know marina phenomenon kind of gap place like a direct you know ceremony but never let's say in a neutron exciting spectrum you are supposed to see gap and I find as I said discussed this you know somehow gap place you know gap you know those kind of a reflex fluctuation into two kind of marina okay or you can calculate you know thermodynamic you know quantity of you know can't understand and I don't know how tough it is but according to my friend Motome you know he developed a special kind of methodology to calculate thermodynamics of those active you know state and according to him yeah so the dynamic signature you can classify 3dg at high temperature everything disordered thermal disordered okay this is kind of red region and then you know around the you know zero sets type interaction okay uh serromagnetic type interaction okay so with uh you know temperature of type interaction you know spin start you know correlating with each other but still you know it's kind of a summary disordered you know state okay so correlation develops but still kind of a disordered and eventually in the blue region blue region uh you have kind of ordering with g2 flux as I said the g2 flux is kind of local quantity and defined you know for each hexagon and at low temperature you know they tend to order and that happens but this happens you know at you know very low temperature as you see like 10 to the minus second 10 to the minus you know fourth of you know ketamine interaction and in general in the existing compound ketamine interaction is over the order 100 k 100 k okay so that means one here is you know 100 kb and the flux ordering takes place you know one percent of ketamine interaction that means one k okay and this is you know 100 milik k and this is 10 milik kb okay so this flux ordering and the real you know like this function should show up you know at you know very low temperature reflecting a disorder of this g2 flux okay and they calculated the specific heat and in a kind of a disordered you know correlated the spin phase it's like you know classical spin you know you see almost a linear behavior but at you know low temperature you see where they find anomaly okay and this is kind of related to ordering of flux g2 flux you know plus minus one each you know hexagon okay and if you calculate entropy okay you divide the specific heat by temperature and integrate you know this area over you can calculate entropy and they calculate the entropy associated this you know low temperature peak okay from purple to blue is you know exactly 50 percent of our low too okay 50 percent of our low too okay or maybe pasting you know 50 percent of kb log 2 right so each spin has you know choice up and down so they have in kb log 2 entropy and this you know you know ordering of flux carries 50 percent that means this low chi and mylarna carries a 50 percent of a spin entropy they say you know it's some sort of a reflection of again fluctuated fractionalization of you know spin one half you know moment okay so you have kind of matta pheromone you have you know it and you know pheromone and this is related to ordering of localized your mylarna pheromones you know carries a 50 percent of entropy okay and as they say it's kind of a signature of fluctuation okay but somehow for pure qtf you know magnet you know we know what it is and we don't have you know confusion of a gap okay and we know how those you know physical property behaves okay that's kind of a nice part of qtf actually yeah so sign of a interaction could be either positive or negative so even you know anti-fellow case you can draw exactly the same so no no difference yeah so in the sense that this you know ijig pair formation is kind of a sense okay so so somehow this is kind of a summary of kind of concept part okay and so this can town spin liquid is you know like a conventional magnet okay you have you know fellow anti-fellow or I think and this is a typical example of a block symmetry spontaneous block symmetry and the spring entropy kind of quenched at the transition but can town spin liquid uh no magnetic ordering no symmetry breaking and that remains you know countermechanically disordered and we have kind of more than one kind of a quantum spin liquid but anyway so spring entropy quenched you know they're kind of gradually so uh in some sense uh you know what I said it's a no magnetic ordering no symmetry breaking so we are searching for nothingness okay but somehow this is uh similar to the concept of jam doing what is then maybe Asian friend you know might know what is jam and actually you know if you visit the Japanese temple in Kyoto some of them are Zen temple and you see garden like this in stone garden like this and this represents you know concept of Zen meaning there's nothing right and this Zen tell us go to the state of nothingness okay go to the state of nothingness that's kind of important okay uh don't think okay this is don't think go state of nothing uh then uh you see hidden reality okay and uh somehow we are looking for state of nothing in quantum spin liquid but once we reach a state of nothing uh we will see hidden reality okay this is nothing but the central dogma of Zen you know concept and we should see reality uh exotic elementary exercises you know like fluctuation but that's why I like this quantum spin liquid as Japanese okay so yeah when I was high school student I refused to take exam and my high school was related to Buddhism so I was sent to Zen temple for two days and you have to sit still and don't think in anything go to state of nothing that's you know how you learn Zen concept okay and if you move you know priest is going to hit you it's a kind of tough you know punishment okay but now uh okay so as you know yes no it's not real sometimes faith transition yeah no no not you know faith transition not faith transition yeah I say flux ordering but yeah no no no no so in case of 2d type there is a no no faith transition okay it's like Zen you're nothing but of course you have a kind of a characteristic temperature and this corresponds to kind of ordering of flux okay so there are kind of excitation of you know excitation uh in uh locate my own channel and uh below that you know gap temperature you know you start saying yeah yeah very good question yeah but my understanding is like you know metal at the height of a there's a kind of a family excitation and at you know tco zero it's completely family degenerate and I saw the station like that and of course there is a kind of characteristic temperature for kind of family degeneracy however we never quite you know ordering and perhaps you know we don't we don't have you know any you know kind of order parameter here okay uh yeah I don't understand okay uh I'm sorry actually Yonbaki kind of gone I lost you know most important consultant here but uh there is a three dimensional architect system which I'm going to talk and in this case uh they categorize the same and they observe the you know thermodynamic you know faith transition and but the term means uh you know in case of a three dimensional architect you know quantum spin liquid you know has kind of redefined the phase and the path to order parameter but the physics uh you know uh I don't need uh my consultant question yes uh could you speak loudly please uh yeah so all the spin liquid you know should have kind of long-range kind of entanglement yeah okay so now I finished uh you know an easy partner for me okay now I'm I feel a bit more easier to speak about this uh let me speak about uh you know uh how to bring at all kind of concept into reality okay and in the afternoon I'm going to talk about existing compound okay but let let me do only kind of set up for theorists okay okay so this is uh you know uh kind of review article by patrically uh 10 years ago and then he said the an end of the drought of quantum spin liquid that means uh we have you know quantum spin liquid are the kind of reality actually you know around 10 years ago we started you know discovering realistic spin liquid you know candidate and from now on you know I'm going to talk about how to materialize those you know concept in real compound okay that's my job okay okay and I'm going to talk about organics you know inorganics you know oxide you know in this afternoon but before getting into uh realistic part uh let me try to make you feel a bit easier to handle those different kind of lattice okay so like a typical you know playground of those you know fluster lattice is like a triangular lattice Kagome lattice you know pyrrole lattice and maybe if you are kind of a theory student you may feel you know we may need a very special chemistry uh to realize you know this kind of lattice okay but I want to say okay take it easy actually you know uh triangle lattice you know here and there in the real world that that's what I mean okay so let me spend uh you know uh three four minutes you know for that uh before the break so uh first of all everybody even a theory colleague you know must know uh sodium chloride structure you know right yeah and uh normally you know you understand the you know this uh sodium chloride structure uh kind of cubic crystal structure right and you often consider this you know uh one zero zero zero one zero zero one direction right that's kind of normal way but why don't you take a look at you know along you know one one one direction you know highly symmetric direction and if you take a look at the sodium chloride structure from you know one one one okay you know uh the first layer blue layer actually you have you know uh okay let me consider nickel oxide okay uh so you know sodium chloride uh structured material and this is a blue kind of auction and the first layer if you do kind of atomic cliff uh you find the triangle lattice or auction you you can check it by yourself and the next layer okay is you know triangle lattice or nickel okay so like if you know nickel has a magnetic moment you have you know triangle lattice you know magnet you know here okay as uh nickel layer and the next layer is again kind of auction and uh so uh along one one one direction so if you kind of rotate your axis one one direction uh you have stack of uh nickel triangle lattice auction triangle nickel triangle auction triangle okay and there are you know thousands of compound which takes you know sodium chloride structure and everywhere you find the triangle lattice but of course uh this you know coupling along you know one one one direction is very strong so uh of course you know as you know you imagine from cubic crystal structure you know uh this nickel oxide is a three-dimensional magnet okay but of course you know uh we are not that stupid uh maybe you know you replace you know half of a nickel with a lithium you can do that right so there are magnetic nickel layer here and there and you replace you know one out of two nickel layer with a non-magnetic lithium layer okay so nickel all become a lithium you know 0.5 nickel 0.5 auction uh then you know uh nickel triangle lattice is kind of well separated then you can create a two-dimensional now nickel triangle lattice and the chemical formula lithium nickel O2 okay this is very famous uh triangle magnet okay so it's just a super structure along one one one direction and you take your nickel triangle lattice out okay that's how you make it and of course uh nickel triangle lattice okay uh if you replace okay one out of three nickel with a non-magnetic lithium uh you can create a hand cover like this okay like it is okay so you replace the half of a nickel with non-magnetic lithium now I replace you know one third of a nickel with a non-magnetic lithium that's how I can create a hand cover like this and this is nothing but the guitar compound okay all related to sodium chloride okay so always you know they start from sodium chloride you know triangular plane and we can manipulate using chemistry or again this is a sodium chloride structure and in a sodium chloride structure you know if you connect you know only sodium atom okay you find the tetrahedral right so in the sodium chloride lattice you connect you know only sodium ion then uh you create a tetrahedral like this and if you take you know only this tetrahedral out from sodium chloride structure you create you know lattice like this okay only corner share the tetrahedral you take out you see this lattice okay this lattice is not called the pylochlor lattice okay structure of pylochlor spinel oxide so if you forget about the pylochlor structure start from sodium chloride now if you take a look at the pylochlor structure along again one one one direction okay now uh you see uh okay stack of triangular lattice and the Kagome lattice so this is a pylochlor structure along one one one is you know stack of big in triangular lattice and the Kagome lattice so like if I use the same technique like replace you know part of it with non-magnetic ion I can create triangular lattice or I can create a Kagome lattice starting from this pylochlor lattice and this actually you know how I make Kagome compound okay which you know I'm going to talk in this afternoon but you know somehow sodium chloride structure is quite you know common you know structural category but out of that I can create all the family of triangular lattice okay so my message just you know theory colleagues take it easy okay you know whatever you know structure you create we can make it okay so I think you know in the kind of first part let me stop you know here take question