 Okay, so let's start our afternoon session. The speaker is Chung Ho Chung, and he's going to tell us about the mechanism for a strange metal in rare earth intermetallic compounds. Okay, thank you. So first of all, I'd like to thank organizers for this invitation. So, in this talk, I will describe possible mechanism to realize this very exotic strange metal ground state or strange metal face in the context of the heavy firmly on metals. This work has been published here in collaborations with my two postdocs, Dr. John Fan Wang and Dr. Yong Ye Zhang in Taiwan. So, so I will first give you a very general introduction to strange metal phenomology in the context of the heavy formula and say cuprates. And then I will describe this particular material that we will focus in this talk, which is the serum palladium aluminum compound compound, which is a frustrated condo lattice compound, which shows a strange metal behavior. And, and then I'll describe, you know, a mechanism for such a strange metal face to appear, which is based on the fluctuating condo stabilize critical spin liquid in the context of the anti pheromaniac condo Heisenberg lattice model. Okay, so then I'll give you a summary. So, as you all know, and it's well known that the non firmly quit behavior appears often near a quantum critical point. In this case, the famous cases, the terbium rodent to silicon to is a heavy vermin metal. And the tornado shape of this so called strange metal region persist all the way down to zero temperature but only at this critical field, which separates this to stable faces one is the anti pheromaniac from the liquid phase. On the left on the right, it is a heavy from liquid with the condo correlations. So this, this kind of a strange metal behavior at the final temperature could be observed experiments across a variety of materials. But, you know, this stays really unstable when temperatures is getting lower and lower until you reach very unstable quantum critical point. So this is a very unstable settle matter. So that's the first message. Okay, so the definition of a strange metal. Phenomena are two folks one is the T linear stability. Any. Oh, yeah. Yeah. Okay, great. So as you can see that the perfect T linear stability persists, you know, from some temperature to all the way to the lowest temperature. And, and that's is the phenomenal number one. Oops, I cannot change the page. The page is frozen. Okay, keep it pressed it shows as a phone. Okay, okay. Yeah. And the second phenomenon was strange metal is from specific he coefficient or gamma coefficient CV over T as you can see here that there is a lot of risk make divergence. There are a lot of temperatures for such a strange metal material, but sometimes it would follow up by power loss singularity is available temperatures. So, so this are the two things that people call this strange metal. And this kind of phenomena occurs, you know, across the variety of strongly coded electronic systems. For example, the Q praise as shown in an earlier talk by us that is the Q praise which shows perfect linear, you know, from, you know, 150 until all the way to the lowest temperature. And more, you know, equally important is the gamma coefficients can see here that the, you know, log T divergence of this gamma coefficients for this, you know, Q praise persists all the way to low temperatures. These two for me phenomena have to come together. And to explain this phenomenon. We should focus not just the linear theory stability but the summer dynamics also very important, and also quantum critical point. So that's the main message whether or not there is exist quantum critical points somewhere near this critical another issue. So, and this methodology exists across, you know, many different materials such as organic subconductors and ionic ties and so on so forth. Okay, so, but recently, even more exotic strength metal phenomenology occurs when we have a stable strength metal ground state, meaning in this material which I focus on. This T power law behavior in restivity persists all the way down to almost zero temperature, but more importantly, it extends, you know, for finite range in this tuning parameter, for example, pressure or the few. So remember this, the terbium rodent to silicon to tornado shape ends at a quantum critical point, but here is not is extended to the finite range in field and pressure, it indicates a very exotic possible strength metal ground state. So, so that's the really, you know, exotic about this phenomenology. So, so how to stabilize this very unstable stretch metal phenomena is the issue. Okay, so, and another example of this stretch metal phase appears in Germanian dope to wire as you know if you dope this wire as by Germanian, you will see extended region of here. So the field that you can see that the nail temperature is going down to zero. But before they have it from liquid forms, there is a finite range in this field that there's no magnetic long range order. And at the same time, the P linear restivity persists all the way down to zero temperature. So this is another exotic strength metal phase. And at the same time, this specific he coefficient also diverges as a law gripping in temperature and followed by Apollo divergence. So, you know, in earlier studies of this G one s, you know, there, there are some observations that this transport and thermodynamics, which shows a stretch metal behavior live in a different temperature window. Okay, so the transport is the chat sector. And the, you know, some of the dynamics may come from, you know, this, the spin sector. So it indicates that maybe a break up the quasi particles into the spin and charge sectors in this very strange stretch metal state. And the general question that we want to address is how can a stable strength metal phase exist in principle, given the fact that the strength metal properties mostly emerged from unstable quantum critical point. So that's the most exotic, you know, property of this material. And can this phase emerge from the competition or collaboration between a counter screening, and it's been liquid state. And with the physical quasi particle effectively get fractionalize into spin, spin on and charge or condo hold on expectations. And the strength metal phase is located is closely related to the critical fluctuations of either excitation so spin charge separation scenario is it relevant or not. And finally, is there omega p scaling in a dynamical properties for this material, which is a signature of a quantum criticality so the omega p scaling is again another very important signature to pin, you know, down the, you know, system to be in a quantum critical point or phase. So let's go back to this material that we focus on. So this is a serum planion lobenin compound on the fuel and the pressure. And this is the heavy Fermi metal and a crystal structure. And it looks like the, you know, this Kagami lattice, where the serum atoms are sitting. So the serum carries 5D and 4F electrons which could lead to the condo and also so could RKK y interactions which I will talk about later. As I show you the transport properties show this extended region of quality linear stability. But at the same time you can see the, you know, the end of this paramagnetic states there is a condo breakdown transition which I will talk about in just a moment, and this transitions play a very important role in theory to actually give rise to some microscopic account for this behavior and the condo which is about five Kelvin. And the stool faces are anti paramagnetic metal and heavy from liquid was a condo effect, and both red regions shows the square behavior. And so this magnetic structure of this material are a little bit complicated, it consists of icing coupling. Among serum atoms, and they're three dimensional. So, along the C axis, we have anti paramagnetic icing coupling. So it's give rise to this CW type of this long range order. And in the AB plan, the Kagami plan, it consists of two icing chance with opposite spins, which are marked by blue chance and red chance. And along the blue and red chance there are paramagnetic icing type of coupling. But there is an anti paramagnetic icing coupling between this two chance. So it's a bit complicated is J1 and J2 and also, you know, C axis anti paramagnetic coupling. So the long range order is probably due to this C axis, you know, anti paramagnetic coupling. So this long range order could be easily suppressed by apply the field of pressure and that's how they observe this paramagnetic phase. So this is a global phase that has material in terms of pressure and field. So you see that, you know, between this anti paramagnetic long range order phase and heavy firm liquid there exists, you know, this finite size window, over which we can see non firm liquid behavior so this is not a point but the face. The green and yellowish regions are all this stretch metal face. So experimentally, you can tell the field of pressure along this arrow direction so that you across a finite range where you see this non familiar with face. What is the blue line. So this, this line. Okay, so this is probably the crossover between a small and large from the surfaces, which is due to the condo breakdown transition. Okay, so the so called spin liquid or paramagnetic behavior is shown from several different observations. The first one is AC spin susceptibility as you can see from this figure that the, you know, this, as you lower temperature the AC spin susceptibility first arises and then saturate. Okay, so which, you know, looks like a poly spin susceptibility occurs here which indicates the fermionic excitations as a spin excitations and also, you know, it shows the signature that's been liquid. Okay, in that paramagnetic window so this behavior also was observed under pressure as you can see that between this new temperature and a maximum temperature of this susceptibility that there is a finite window in temperature range, where you see this paramagnetic or spin liquid like behavior. So recently it's just this year. There's a new SR experiment on this material is on dope one, which indicates indeed this is a spin liquid type, because the new SR signal. It shows, you know, exponential decay of the spectrum with some oscillations, if the state is in a long range order phase. But, you know, below, you know, above the critical pressure in this SL or spin liquids region. So, this new SR doesn't pick up the oscillation. So there's no oscillation, meaning no long range order. And it is indeed signature of a paramagnetic spin liquid phase. Okay, so so this phase is real. Yeah, this is also metallic. So it's a metallic spin liquid like. Of course, this is just a possibility to really, you know, have a smoking gun evidence for spin liquid you need more evidence such as neutron scattering so on. So, but this, you know, just experiment just tells you that, you know, spin liquid is a possibility. Or paramagnetic states is a possibility. So the condo breakdown transition from this whole coefficient measurement this material shows a jump. You know, between a small firm surface, a low field to the large from a surface at the high field. So, it clearly indicates, you know, a very sharp jump transition between, you know, the two sides of firm surface which indicates that's, you know, if there's a condo effect, which I'll talk about just a moment, and this every electron participated from the surface the firm surface will get enlarged by condo disappeared and the firm surface is small. So it's directly indicating that, you know, whether or not of condo effect play a role here. So there's a transition. You know, near the end of the paramagnetic phase that this is a condo breakdown transition and we could define this crossover scale. B star. Okay, so, and in the thermodynamics. And it shows a two logarithmic divergence of gamma coefficients I mentioned, because you can see here from this, you know, plots that they dope this material by Nico and between this 14 and 20% of a doping. So you can see this logarithmic divergence of a gamma coefficient but you can see really from this plot that in the transport you got two different colors, greens and oranges. And which indicates that there are two kinds of, you know, nothing from liquid behavior here is the same thing. So if you make a fit to this, you know, this figure you can see that there are two kinds of logarithmic divergence which I will address in just a moment. First, at intermediate temperature range that you could fit this data by a logarithmic, you know, curve and at the very low temperature close to the ground state you can also fit this by another logarithmic divergent curve. Okay, so double logarithmic curves is seen here. So the, the talking about this origin of this effect, we should go back to the condo in competition with the RKK why so in the condo lettuce we know that the DNF electron can hybridize, you know, which leads to the condo cloud and this will enlarge the firm surface, and also the condo correlation can mediate the, you know, nearest neighbor spin spin couplings between the local moments and which we call this RKK why. So this RKK why is usually anti paramagnetic in many heavy permanent compounds. So the competition between the still, you know, can describe quantitative features of the strange mental in many heavy from your compounds. So this is the Doniak base diagram based on this long range magnetic order phase in competition with the condo and there exists a kind of critical point and above finite temperature, the QCP you can see this strange mental but this is just a standard conventional view of this, you know, system. Remember, there's no long range order in our interest region because the magnetic frustration. And that leads to this scenario, you know, unlikely to occur so we need to revise this scenario that the competition now should be between, you know, kind of a paramagnetic state. In our case we propose a spin liquid metal in competition with the condo. Are you fair. Yes. So, good question. Thank you. So remember this AC speed sensitivity for audience. So, so for spin liquids, you know, doesn't shoot up as a cure device or as a paramagnetic material right is is saturate. Okay, it doesn't go down to zero either. So this is really the finite value. So this is the indication of the spin liquid life behavior of course it has other possibilities but this greatly distinguished this huge. Right, right, right so this doesn't include exclude this metal. Okay, it's just. Okay, thank you for the question. So, so, so then, because of this, we, you know, try to find out what are the key quantum critical fluctuations to give rise to such a strength metal behavior. So, we propose that this bosonic condo fluctuations, you know, in combination with the fermionic RVB spin liquid made of a fermionic spinons could lead to such a behavior. So, so we will discuss that in the following. So this is our earlier attempt to account for this Germanian dog the wire as in terms of Anderson says spin liquid, which is a gaps been liquid was the decoupled, you know, the coupled metal underneath, and this states is in competition with the condo. So, and we use this perturbed to the RG scheme to actually quality account for such a linearity restivity. And also this also cross over. Okay, but the this this stays the spin liquid as a gap spin liquid was a metallic behavior. So this state has not been found experimentally. So we need to find an alternative, you know, other approach. But our earlier study clearly see this linearity restivity can arise from this kind of a scattering of electrons from this condo fluctuation diagram which I will tell you just a moment and this kind of a scattering processes could lead to a T linearity. Okay, and here is our model. We generalize this as you to counter Heisenberg, let's model to, you know, multi channel and large and limit, and on the square that is for simplicity, and we saw this model in a dynamical way. So this is a material consists of the, you know, this isolated conduction electron bars, which we call this local boss approximation, and locally this conduction electron could, you know, be this this beans on a local conduction which is defined by a condo effect by local moment which is shown in in here as F and this condo effect is described by a fermionic, you know, by quadratic term here, and the so called Heisenberg RKK Y term is written in terms of the, you know, particle particle, in the larger type of RV bees been liquid, and we generalize this model to SPN across as you came as one. And we saw the model in the larger and multi channel limits, where this Kappa is K over and is fixed. So, so and then we further put this channel symmetry to this multi channel condo term. You know, the purpose of doing this is to favor the fully screen condo from liquid in the condo region, but J condo is much larger than J RKK Y. On the other hand is body channel fluctuating condo term will give rise to the non familiar with that. Okay, so this is a marriage between these two terms, one is the condo from liquid, another is the non familiar great which can be induced by this multi channel condo term. Okay, so first we do this at a mean few level, we decouple this condo Heisenberg term in the by the hopper strong which transformation, and we define this mean few other parameters, which are to both only feels one is was only going to be made of a fermionic spin on like this and other is both only condo collisions, which is the conversation between the conduction electron and the local election like this. And then we go beyond the mean few. You know by decoupling this condo have position term in terms of a condensate part because this is the boson field, it could get both condensation, or it could not get the both condensation. Okay, and plus this fluctuating condo term, and this plays a very important role to lead to this non familiar physics. So solve the model by including the self energy of those, you know, local fermions and conducting electrons and this whole long condo fluctuating field self consistently in this Dyson type of equation and which is in some sense similar to the DMFT. Okay, and we solve the model in the larger limit multi channel limits and the mean few variables are solved by the seven point equations like this. So this is our solution. As you can see that we have, you know, all the phases that we need this condo phase on the right when the condo is larger than the stage. So we have a spin liquid yellow phase where we are in the other region this RKK Y dominates, and we have a pink region, which is a coexisting phase between the condo and RVB and this is the superconducting phase, which was, you know, proposed long time ago. In the context of the cupra and the other spinons and hold on spectral functions are gapless. And in the yellow region, which is the, the phase that corresponds the stretch metal phase, the experiments. Okay, so as you can see that's the, the whole on the spin on spectral weights are non gaps, and in particular this F spin owns show a whole lot of singularities, because of this spin on Fermi surface, you know, have filled where this, you know, effective spin is one half or campus one half here, which shows a particle for symmetry. And the whole on spectral weight also shows, you know, power law vanish but it is not gap. So both whole on spin owns are not gaps. So this is the gapless spin liquid states made of gapless, you know, whole lungs and gapless spin owns and the, the spin on spectral weight shows a lot of risk make in energy divergence. And so, and there is a critical point GQC, we separate superconducting phase and a yellow stretch metal spin liquid phase and this gray area. You know, it is the non film liquid strength metal region associated with this GQC is critical point. So, and to illustrate this, this kind of a stretch metal phase, we use a cartoon picture with this Anderson's RVB spin liquid couple to the whole long field and also the electron field through this condo fluctuating terms. And these, this term stabilized the spin liquid in, in a, you know, in a stretch metal region so so and but this physics has been discussed long time ago. In the context of this condo stabilized spin liquid close the magnetic instability at the mean few level, and this theory was proposed by Professor not on entry and there's Coleman in 1989. So thanks to this mechanism. So we think that our mechanism is very close to this one. So this magazine says that the spin liquid state, although shows a higher energy than the anti pherominated states, but with the help of the condo habitation, and this energy of spin liquid could actually, you know, be lower than the long range older phase and this phase is a superconducting term when both condo and spin liquid exists. And so this superconducting state can account for a cost of heavy from your superconducting state. Okay, so, you know, by means of the condo habitation the here is very similar. So, instead of a mean field condo turn, we couple the spin liquid with the fluctuating condo turn. And indeed, we find this, you know, spin liquid is not ordinary split liquid but shows a strength metal behavior. So this is the first, you know, observable that we calculated in this strength metal phase that this electron sketching rate which is proportional to this imaginary power of the T matrix, and which is this diagram here, and which is proportional to this electrical resistivity when it's connection bars are connected. So, as you can see that we do see this to kind of power low behavior one is the intermediate temperature range, which is sub linear in temperature and at a very low temperature it is super linear. Okay, the power exponent is 1.6. And we do find omega of the scaling the T matrix, we have two kind of omega of the scaling. One is that very low omega of the T ratio another is in the intermediate range which corresponds to the yellow and gray region respectively. So, and you can compare our results with the experiments which shows clearly this tool, you know, color, a golden region in this, you know, strength metal phase one is the greenish another is oranges. So which shows two different power law exactly. This is what we found. And we also have results away from the particle symmetry by tuning away the kappa, you know, from one half and we do find in our parameter region that this team actually shows two linear behavior. So, coming back to the thermodynamics we calculate is the entropy and species he coefficient, and we do find two logarithmic, you know, scaling regions. One is intermediate region another is a very low temperature region, which agrees quite quickly, very well with what's experimental has been observed. And this logarithmic singularities, you know, the origin of that we find, we think this is probably due to the fun whole singularity of the 2d spin on Fermi surface. And we also calculate this static spin susceptibility low temperatures and we also find this T log risk mean divergence and dynamics means of ability shows a plateaued at low temperatures which indicate this is consistent with the policy spin susceptibility. And again, it's a logarithmic temperature. And so, so what is the quantum critical about this phase. Well, this is the most general phase diagram in terms of temperature and kept up with the fact of spin and also this ratio between take on the jlpky, as you can see that this strength metal phase live along this graph I could one half line, which is a particle symmetric line. So, along this capital direction, we have a quantum critical point exactly at traffic one half. So this is a quantum critical point, if we are looking at this phase diagram along the capital direction, but if we fix the capital to be at one half, and go along this direction of this capital constant. And this quantum critical point extends to the finite range in coupling constant space so it is a quantum critical phase. So it is a quantum critical point, and also it is a quantum critical phase, depending on where you look at the space diagram. And this strength metal behavior persist, even away from this particle symmetry point, as you can see from here. But on two sides of the transition we have a gap spin liquid which shows the variance bond solid. And also we have a gap on the spin on the whole on a spectral function. Okay, so we check stability of this transform metal phase. And first the, you know this gap has been liquid made of a fermionic spinons, it's actually you want to be liquid. And we know that if the you want to be liquid is gaps, then we have instant on effect which will make this, you know, unstable against the standardization, but fortunately we have a, you know, spin on from the surface. We have earlier studies shown this paper that once we have a spin on from the surface, and the instant on effect is actually irrelevant on the RG so which stabilize our critical spin liquid. And we also, you know, find this, you know, what are these these phase diagrams of finite n and finite k and they all look quite to be the same. And we also go away from this particle symmetry by considering the particle or symmetry of a conduction band, and the result is also the same. And we also go away from the particle symmetry point of the local fermions. And as I just show you that this behavior persists up to the final temperature and then it exponential decay, because of the gap has been on hold on. Okay, and what about channel symmetry. Okay, so I assume that this, you know, condo coupling shows, you know, multi channel and one of the channel has a larger kind of coupling than the others. What, what about we make all this coupling constant equal for all the channels, and this is so called a channel symmetric large and kind of Heisenberg model, and from earlier studies, join this paper that the ground state should be the over screamed non firm liquid. And same thing here so we find that this should be a over screen non firm liquid. And, but this yellow region still there. So this non firm liquid stretch metal phase, which is the spin liquid couple the condo fluctuation still persist. Okay, so this very robust phase. Okay, so, so let me just finally just try to make some connections to the Q praise. And as we can see from this plot that this plot has been shown many, many times that in Q praise close to the critical doping. There is, there was, you know, observed that there's a jump of a whole coefficient from the lower value to the, to the larger value indicating this Fermi surface is reconstructed near this critical doping and which, you know, a similar period, this kind of a condo breakdown scenario that this Fermi surface evolved from a smaller to the larger value. And but more recently, there are more evidence of another Q praise materials which shows very interesting stretch metal face. And as you can see here, this theory of relativity in good place, no persist to the lower temperature and over a finite range in doping. Okay, starting from 20% to almost 30% 30% this whole range so stretch metal. Okay, so it's called a stretch metal face. So this whole coefficient does not show the jump. Instead, it shows a smooth crossover on the lower value to the larger value. Okay, so it brings an interesting question whether there's a quantum critical point, you know, underneath the superconducting dome, or whether this is a non familiar face, or, or a quantum critical point is that is the hot debate at the moment. So, so this is still this debate is still going on. Let me summarize my talk. So, in our simplified a condo has simple model by a large and multi channel approach, we find a stable stretch metal face appear in our parameters space and, and this phase emerges because of the coupling in RVB likes been liquid to account of fluctuations and which shows in transport this quasi linear tea sketching rates and also T log risk link divergent specific heat, where both phenomena has been observed in Syrian plate and aluminum compound. And, yeah, so I before the end of the talk let me acknowledge, you know, various experts that I discussed with the Joe Thompson and friend staglish and congratulations to Professor friend staglish this low temperature world. And theorists team LC and Pierce Coleman, but just for it. And Stephen Kushner. So thank you very much for attention. Okay, thanks very much. Questions. Actually, I have a question from online. Yes, yes, please. Hi. You say that this heavy firm and system is nearly 2d. Now. Actually, it. There is some coupling between the two dimensional components. So, this coupling should introduce some kind of lower temperature cut off to the specific heat divergence. It seems to me you attribute to the banova singularity of the spin liquid component. So this banova singularity should be lifted by this small interlayer coupling. And this should be reflected with the specific heat behavior at low, very low temperature. Is there any chance to see this. Yeah, thank you for the question so indeed so our models is a bit simplified we consider a 2d model, but the real materials three dimensional I agree. So, the most important, I think, say features come from this layers of those materials, and I also agree that perhaps there is a cut off a very low temperature because of an interlayer coupling, which we did not take this into account in our theory. Yes. Much much more dumb question I'm sorry, but I wasn't able to understand when you're talking about this critical line. What exactly was the sharp definition of what's critical there what is zero or infinity there that's not zero or infinity, you know, in horizontally infinitesimally away. Is it just because of the observables is there some quantity some correlation function that diverges only at that point. Yeah, very good question. So this is the, you know, your question right. Okay, so we go along the Kappa direction, then this is the crossover that we found. Okay. Kappa is effective spin on each side effectively in the larger language. Okay, so Kappa to one half means that we have one, you know, spin one half local moment on each side, just spin one half and that's your two limit. So if we change this value of Kappa, and we still see this non familiar behavior but it's bounded by this kind of a parabola. Okay, and out of this outside of this region. We can see that the spin on the whole ones are gap out. So the signatures of this critical regions defined by whether you can see this exponential decay. That defines the boundary here. Is that answering question. Yes. There's one. There's one. So, even you showed the crystal it was not clear. Is there inversion symmetry in the crystal or is it a non centrosymmetric crystal. I suppose this is the same inversion symmetric material. So, at least we don't consider inversion symmetry breaking our theory. So if I look at the crystal it doesn't seem like the serium atoms are at the inversion center so where is the inversion center in this crystal versus the inversion center of the. So if I look at the site, the pink ones are the, no, the pink ones are the serials. Yeah, don't seem to be inversion centers right yeah where is the inversion center is it off. Yeah. So, it's not easy to see here, this plot so but you know, I am not aware of the, you know this discussion about this inversion symmetry breaking in this material at the moment, maybe there's inversion symmetry breaking. Okay, so what I'm going for is that if you have an inversion center and the serium is not at the inversion center. And then there are at least two sub lattices of the serium. And if you, if you then think of the two serials as sub lattices, then wouldn't you have to think of two channel condo models because the anti symmetric and the symmetric Okay, I'll give you two different condo channels which are here. Okay, yeah, so I think this this the two forces one is from experimental point of view one is from theory point of view. Okay, so from experimental point of view this is what it is. Right. So you have icing there are making the long blue and red chain there's anti parameter between these two. Okay, so. Well, so. And there's a missing, you know, make a moment in the middle, which is caused by frustration. Okay, so it's not clear whether we have a two side per unit cell here. Okay, so what we are doing here is just simplify this. You know, material by considering just a square lattice condo Heisenberg lattice model and what is square about this. Well, if you look at this anti parameter, you know, exchange company, it's lived along day two, which is not on a cognitive basis. And if you look at the c axis anti parameter coupling. And, you know, you could do some, you know, say hand waving or some probation calculation that it may induce anti parameter spin spin couplings on the day one. So the underlying anti parameter fluctuations is on frustrated. You know, from by j one day two. So, so that's probably is a coincidence, but it's very good coincidence that we consider a square lattice. And that's perhaps is the reason why they see this always make divergence in gamma coefficients because of this square like, you know, structure in your spin fluctuations. And also the counter fluctuations. Okay, but the frustration plays a very important role, which surprise, you know, one on one hand is long range order. On the other hand, you know, to give rise to this, you know, fluctuating counter to play around. Okay, I think there's one question from the chat. And thank you for this nice presentation. Can I ask a question. It just just once again we'll just finish this one. Hello. What is the difference between spin liquid and spin. Well, I'm not expert on spin gas. But I suppose from the spin spin correlation you could distinguish. I guess the stinglass has frozen moments frozen moments. Yeah. Yes. Yes. So you wanted to ask a question. Yeah, I'm sorry. I missed the beginning of your talk but are you assuming the spin fluctuations are, which are giving rise to linearity resistivity they're completely momentum independent. The spectrum of them. Is that correct. I mean there is momentum independent. I mean the spin fluctuation spectrum has no momentum dependence. Oh yeah, here we are considering a moment in independent calculation, which is the DMF feel like we consider a local bus approximation. So no K dependent in our theory. So, in other words, the momentum is integrated out to some extent, and we are generalizing our approach to consider the K dependent self energy. And if we have that down then we could discuss the K dependent foundation. Yeah, but there's also vertex directions to the conductivity associated with drag effects that it's not simply a question of looking at momentum dependence of self energy. Anyway, the other question was, you had a spin on for me surface. We know that 2D the spin on for me surface has a T to the two thirds specific heat because once you do gauge fluctuations. What about that. Right, we did not consider the gauge fluctuations. But for this argument that I, I showed that the from say some series earlier studies that once we have a spin on from the surface that you engage fear will not quite change this spin liquid. So we did not consider that effect in our theory. Okay, thanks. Yeah, so just for clarification, you said to think you said momentum independent and momentum integrated. Which one is correct momentum independent spectrum or when you solve for self energy you integrate our momentum and sorry about confusion is momentum independent approach. Okay. Well, so sorry, I take this back. So, what we did is, we saw this local green functions and local self energies. Of course there is a dispersion in the conduction bands, which we already integrated out. Yeah, we don't have the information once we solve the local green function and self energies. Yeah. But, but I think the question is about the momentum dependence of the spin question. The momentum depends on dependence of the spin. How does the stability has a momentum dependence or not is experiment theory of the experiment scattering are the next scattering experiments showing how spin behaves momentum space. Oh yeah, you mean experimentally from neutron scattering. Um, I, indeed, it should show, if you this has been liquid show this broad distribution in this neutron spectrum. And that I agree. And in our theory, we cannot capture this as I mentioned this self energy and greens function are solved locally. So, there's no way in the present theory that we could account for such a momentum frequency dependence in the neutron scattering data is that what you're saying. Mm hmm. Yeah. Yeah, so at this point we cannot address this issue. Right. Thank you for your question. Okay, so let's take to go again. Thank you. Yeah, it's a it's a poster. Yeah, presentations now. So I think we're going from a to K. Yeah, and, and the right.