KITP - 16

Quantum Phase Transitions

Participants
Blackboard Seminar
Tuesday Seminar
Final Wrap Up Discussion

Week 16.
April 25th - 29th, 2005

Bloggers: Piers Coleman, Andrey Chubukov.

	Final week of the workshop, but a week full of activity. On Monday, Victor Yakovenko gave the blackboard seminar on "Fermion condensation" - (a proposed instability of the Fermi surface where the quasiparticle residue remains finite, but the quasiparticle velocities go to zero, to produce a flat band). Our experimentalist of the week was Gilbert Lonzarich, from Cambridge. Gil gave a fascinating overview of quantum phase transitions, focussing predominantly, but not exclusively, on ferromagnetic transitions. During his talk, he made the interesting proposal that many of the observed ferromagnets are quite probably, long pitch heli-magnets. On Thursday, we wrapped up with a discussion of a long list of questions posed by Gil's talk, followed by a brief presentation of some of the research projects that have been going on during the workshop.
As we finish blogging, we should mention that Tom Siegfried, the KITP journalist in residence, has been looking in our meeting, and has encouraged us (condensed matter theorists) to try to think up new words to explain our field, words that will reach out more to the public, capturing their attention, speaking more closely to the meaning of the phenomenon. Tom has pointed out that words like "Kondo effect" mean nothing to the public - and that as a field, we have been one of the least effective at proposing with good words to connect to our philanthropic sponsors - the public at large. He cited how "black holes" as a replacement for "Self Gravitating Objects", "Quarks" as examples of how imaginative choices of words can capture the public's fascination. Tom gives a quick example of how he might try to deal with the word "plasmon", and has provided a list of words that we need to work on. (How about Zachary Fisk's suggestion that a quantum critical point is the "Black Hole of magnetism?)	For example: PLASMON The quanta of waves produced in matter by collective effects of large number of electrons disturbed from equilibrium. Its the subatomic tsunami that happens when something shakes up a metal's electrons like an earthquake. Plasmons might be useful in designing solar power cells or holographic imaging devices. Tom's list of words: if you have any input on these, please email siegfried@kitp.ucsb.edu
Did we solve the many questions we have posed (see week1, week15)? Not yet, at least, but it is our sense that much progress has been made. New problems have been opened up (see below), new collaborations formed, new and exciting approaches developed. There have also been unexpected recrochements with particle physics, with Scott Thomas' ideas on "emergent supersymmetry", and Joerg Schamalian and Andrey Chubukov's use of methods from the high temperature superconductivity, to quark-color superconductivity. From the many discussions we have had, there is a growing appreciation from those who steadfastly support a Moriya-Hertz picture of quantum phase transitions, and those who have favored a radically new outl.ook, that the truth quite possibly incorporates both points of view. (See discussion by Qimiao Si, week12 ). The discussions and collaborations of the past few months has sewn many new ideas - it is our sense that the papers that follow in the coming months will show how very fertile the workshop has been. Thank you all for attending.

Participants present. Click on participant to read questions that they have posed

Chubukov, Andrey
Coleman, Piers
Haas, Stephan
Ho, Andrew
Khodel, Victor
Krotkov, Pavel
Le Hur, Karyn
Lonzarich, Gilbert
Posazhennikova, Anna
Ramazashvili, Revaz

Schmalian, Joerg
Si, Qimiao
Stewart, Greg
Steglich, Frank
Vekhter, Ilya
Yakovenko,Victor

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Blackboard Discussion. 10am Monday, 25th April.

Dr. Victor Yakovenko University of Maryland	Fermion condensation scenari of non-Fermi liquid behavior.
	On Monday, Victor Yakovenko talked about his recent works with Victor Khodel and others on the "Fermionic condensate scenario of non-Fermi liquid behavior"
Victor began his talk by showing us the data for the effective mass in 3D He-3 films and 2D Si-MOSFET layers. In both systems, the effective mass diverges at some critical density. In 3He, the interaction is short-range, and the mass diverges as the density increases. In Si-MOSFET s, the interaction is long-range (Coulomb), and the mass diverges as the density goes down ($r_s$ increases). Effective mass in 3D He-3 films after Casey, Patel, Nyeki ,Cowan and Saunders, PRL 90 , 1159301, (2000).	Victor also showed data for the spin susceptibility in the 2D electron gas, and argued that the divergence of the mass is likely not accompanied by the divergence of the gyro-magnetic ratio. He stressed that the divergence of the mass occurs in systems with no f-electrons, no Kondo physics, and no lattice. Gyromagnetic ratio of 2DEG after Anisimova et al cond-mat/0503123
He then moved to the theory. He argued that the conventional description of the Landau Fermi liquid theory is based on two assumptions: 1. that quasiparticles are long-lived excitations near k_F. 2. that the Fermi velocity is finite. Under these assumptions, the specific heat is linear in T, and the spin susceptibility is a constant at low T. Victor conjectured that there may be a situation when quasiparticles are still well-defined near the Fermi surface (i.e., quasiparticle residue is finite), but that their velocity vanishes. The vanishing Fermi velocity implies that the density of states diverges. Victor cited a Lifshitz transition as an example of such behavior. Once this occurs, the spin susceptibility and specific heat no longer display generic Fermi-liquid behavior.
Victor describing the toy model.	Victor went on to present the toy model in which fermions interact via an effective Hartree potential f_p,p' which is peaked at q=p-p'=0. The theory can be reformulated as an effective Landau theory, if one assumes that the Landau function does not depend on the quasiparticle distribution function n_p. Victor argued that, under the extra assumption of particle-hole symmetry, this toy model displays a transition between the conventional Fermi-liquid phase in which the effective mass is positive, and the new phase, in which the mass is formally negative. The transition is governed by the strength of the overall factor in f_p,p'. At the transition point, the quasiparticle dispersion is \epsilon_p \propto (p-p_F)^3, and the specific heat behaves as C_v~T^1/3, while the spin susceptibility diverges as 1/T^2/3.
Victor then discussed the new phase, in which the mass formally becomes negative. He argued that the right solution at T -> 0 in this phase yields the dispersion that identically vanishes in a finite range of momenta around original p_F, and the distribution function n_p which is one at small momenta, zero at large momenta, but interpolates smoothly between 1 and zero in the momentum range where the dispersion vanishes. This phase is called a fermion condensate.

He presented the results for the entropy and the specific heat in the phase with fermion condensate, and argued that the entropy tends to a finite value at T=0, the specific heat is linear in T, and the spin susceptibility scales as 1/T. The 1/T behavior resembles Curie behavior, although there actually are no localized spins in the problem. Victor argued that the specific heat and susceptibility data in Ce-based 115 heavy fermion materials can be understood if one assumes that these materials are in the fermionic condensate phase. Answering numerous questions, Victor said that the finite entropy of the phase with the fermionic condensate indicates that this phase probably will be unstable with respect to perturbations. Their hope, however, is that there may exist an intermediate temperature range where the effects of diverging mass already affect thermodynamics, but the fluctuations leading eventually to some other state (e.g., a ferromagnet), and fluctuations that affect quasiparticleresidue and may eventually destroy quasiparticles at QCP are still weak. Whether this is indeed the case is beyond the toy model and still remains to be seen.

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Seminar, 12.30 Tuesday 27th April

Dr. Gilbert Lonzarich Cavendish Laboratory, Cambridge.	First and Second order Ferromagnetic Phase Quantum Phase transitions in Metals
Gil Lonzarich at the "Brown Pelican" Aroyo beach.	Gil began his talk discussing the theory of ferromagnetic quantum phase transitions, as developed by Schrieffer, Doniach, Moriya and Hertz. He cited Ni3Al as a classic example of such behavior. The important point about this theory, is that the spin relaxation rate has the following form which varies as q^3 at the quantum critical point.
Gil showed the phase diagram expected in this theory.Gil pointed out that quantum critical ferromagnetic matter is actually a marginal Fermi liquid, with a quasiparticle scattering rate that is linear in Energy. He pointed out that this observation is due to Dzyaloshinskii & Kodratenko, (76), Baym and Pethick (1991). However, because the scattering is forward scattering, The resistivity induced by quantum critical magnetic fluctuations involves an additional factor of temperature, and varies as T5/3. However, he region of T5/3 behavior becomes very narrow at the QCP. At hgher temperatures, the small angle scattering does not matter, and the resistivity is indeed quasi-linear in temperature. Gil showed data that supported this cross-over from T^5/3 to T-linear in Ni3Al
	Gil then turned to discuss the issue of superconductivity near a quantum phase transition. He showed a generic phase diagram for both the ferromagnets and antiferromagnets. For the ferromagnets, p-wave pairing is predicted, and observed near the quantum critical point in UGe2- the transition temperature dips at the critical pressure, due to the pair-breaking effects of low q transverse fluctuations. In antiferromagnets, d-wave pairing, can it seems, occur in two islands - one around the antiferromagnetic transition, and a second "dome" at higher pressures which is thought to be associated with a valence changing transition - as seen in CeCu2Si2 (see Steglich's talk last week)
Gil then spoke about the important effect of anisotropy on antiferromagnetic quantum critical points, showing the family of Cerium-Indium systems. When one goes from CeIn_3 to the more anisotropic system CeRhIn5, Tc increases, in large part because umklapp pair-breaking effects are weaker on a d-wave superconductor in two dimenional.

	Gil then turned to the predictions of the spin-fluctuation model for spin-fluctuation mediated pairing near antiferromagnetic, and ferromagnetic quantum critical points. He showed how Tc depends on the inverse correlation length. In d-wave systems, there is only a weak dependence on the inverse correlation length. For triplet pairing in ferromagnets, the small -q transverse fluctuations are strongly pair breaking, and suppress Tc close to the quantum phase transition. Gil mentioned that the vertex corrections become very important for afm near the QPT, however they form a very useful guideline for materials research - for the hunt for superconductivity!
Gil emphasized that p-wave pairing is highly susceptibile to pair breaking effects, particularly umklapp scattering, coming from transverse fluctuations. The solution? Go to systems that are anisotropic. This was the key to UGe2, URhGe and UIr, which all show p-wave pairing in the presence of ferromagnetism. All of them have strong uniaxial anisotropy. In UGe2, superconductivity seems to cluster at the foot of a metamagnetic transition, actually a crossover where the magnetization jumps up rapidly by about 0.2 units. Gil made the interesting analogy between this situation, and the superconductivity around the valence changing transition in CeCu2Si2. UGe2, URhGe and UIr all have a tricritical point, In closing the discussion of superconductivity - Gil mentioned the puzzle of YbRh2Si2. According to spin fluctuation theory, this should be a d-wave superconductor- yet there are no signs in ultra-pure compounds. Gil concludes that it may be the presence of local spin fluctuations, which would be severely pair breaking for superconductivity. This is a point of view that enlarges on that given by Frank Steglich, last week.
Pressure -temperature phase diagram of MnSi "Universal phase diagram for itinerant ferromagnets"	In the last part of the talk, Gil turned to MnSi and the T^1.5 puzzle. MnSi is a long pitch spiral antiferromagnet - almost a ferromagnet that we have discussed before in this meeting. Beyond 15kbar, it enters an unusual phase with a T^1.5 dependence of the resistivity. Gil wanted to point out that many "ferromagnetic metals" display this behavior beyond a quantum phase transition, including Ni3Al, ZrZn2, YNi3, MnSi, CoS2, UCoAl, UGe2, UIr It is also seen in the AFM insulator NiS2Sex, also CeIn3, CeRu2Ge2. Is there a common origin? Gil Put up a proposed "universal" temperature- pressure, field phase diagram for itinerant ferromagnets, (or long pitch ferromagnets), with a 1st order "sheet" separating the Fermi liquid from the unusual (paramagnetic?) phase. He suggested that one could locate many systems on this phase diagram. UGe2 is inside the ferromagnetic phase. Ni3Al is a marginal Fermi liquid, well above the ferromagnetic phase. Sr3Ru2O7 is out near a critical end-point of the 1st order sheet. Is the T^1.5 metal a new phase of matter? Gil thinks so. Possible explanations of the new phase are Magnetic rotons Magnetic Heterogenieties. Magnons with an attractive interaction An instanton paramagnet, quantum tunneling between two almost degenerate phases.
Ending the talk, Gil made the cursorary remark, that perhaps all of the so called itinerant ferromagnets, are long pitch spirals. He notes that the uniform susceptibility does not diverge as much as he might expect - e.g, in an appropriate comparison with a ferro-electric- this he suggests, might be because they are all long pitch spiral phases. Work has recently shown that Gadolinium is a spiral magnet (long thought to be a ferromagnet.) Great - so what is it about the melting of a spiral magnet that gives rise to the T^1.5 phase? This is a big open and unsolved question. Gil finished by talking about the future of experimental research on quantum phase transitions. He mentioned a new diamond based system for accessing ultra-high (100kbar plus) inside dilution fridge and also showed the new design for his cryocoolers - these are demagnetization fridges that involve no dilution fridge, with a significant cooling power which can hold the base temperature of 5mK over 12 hours. He thinks even theorists will be able to do measurements!	Gil showing the design for a new diamond-based high pressure rig.

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Final Round-up discussion, 4.30 Founders Room, Thursday 29^th April.

So this is it - the end of the workshop! We began with a discussion of points arising from Gils excellent seminar on Tuesday, after which a few participants (all were invited) presented a five minute resume on the issues and work they've been engaged in at the workshop. For the initial discussion, we discussed a sequence of questions posed to us by Gil Lonzarich. Briefly, these questions were: Why are first order transitions so ubiquitious in ferro magnets Could it be that the spiral state is more common in so-called ferromagnets? Why don't we see a T² resistivity beyond a Ferromagnetic phase transition (why is it T^1.5?) ? Could this be an instanton liquid? Why is high purity Sr3Ru2O7 not superconducting, and what are the phases that form around the critical end-point? Is there a link between the superconductivity that forms around the 1st order valence instability line in CeNi2Ge2/ CeCu2Si2 and the superconductivity that forms around the metamagnetic transition in UGe2 - and could this idea be important to the cuprates?!
Questions 1 and 2 encouraged a strong response from Andrey Chubukov and Victor Yakovenko. Andrey Chubukov briefly mentioned work he'd done in collaboration with Rech and Pepin(cond-mat/0311420), in which they found that the leading one-magnon corrections to the magnetic susceptibility given rise to non-analytic terms in the inverse susceptibility of the form which favor an instability to a long-pitch spiral state. This might be, he suggests, the origin of Gil Lonzarich's suggested pre-ponderance of long-pitch spiral antiferromagnetism. Andrey also mentioned the work of Deiter Belitz, Ted Kirkpatrick and Jorg Rollbuller(cond-mat/0410334), in which spin-wave interactions drive a first order phase transition and a critical line in ferromagnets. Victor Yakovenko also stood up and mentioned work by Benedikt Binz and Manfred Sigrist(cond-mat/0401294), in which the presence of van Hove singularities also leads to a critical end point. This scenario does not naturally lead to a spiral antiferromagnet.	Victor Yakovenko explaining the work by Binz and Sigrist.
Question 4 led Coleman to suggest, following discussion by Dirk Van der Marel, that perhaps MnSi is a more localized spin system than we imagine. The spiral magnet would then be a biaxial system, which could melt via a two stage process, through an intermediate nematic phase. (see Laeuchli et al cond-mat/0412035) . He suggested that this would mean a second quantum phase transition into a T^2 resistivity Fermi liquid (scenario (A) across) Andrey Chubukov asked whether, instead of a new phase,, the temperature at which the Fermi liquid forms might be so low as to be unobservable. In this second scenario there would be no second quantum phase transition (B), Question (4) prompted a number of reactions. We first talked about MnSi - why it is not superconducting. Ilya Vekhter said "Whats the problem - MnSi has no inversion symmetry". Joerg Schmallian muttered something like - "Well - why isn't Sodium superconducting? " Gil responded that spin fluctuation theory did predict superconductivity for MnSi, and certainly for Sr₃Ru₂O₇. He worries that the exceptions may be an indication of a serious problem.....	Two scenarios for MnSi -(A) T^1.5 resistitivity signifies a new phase of matter, with a distinct second quantum phase transition back into the Fermi liquid; (B) T^1.5 is a crossover to a very low temperature Fermi liquid
Question (5) - whether valence instabilities can produce superconductivity - prompted Andrey Chubukov to remark that "charge fluctuations probably don't produce d-wave pairing". Qimiao Si remarked that probably a better way to view the sudden change in density, is as a Kondo volume collapse, not a valence changing transition. At this point, we switched gears, and a few of us talked about the work they'd been doing while at the workshop.
Joerg Schmalian told us about the work he's been doing with Catherine Pepin, Maxim Dzero, Mike Norman and others, on the quantum critical end-point associated with a valence instability or Kondo volume collapse. What happens when the classical critical point associated with a valence transition or Kondo volume collapse is suppressed to absolute zero? Karyn Le Hur remarked that this problem may map on to a Kondo Problem in a non-ohmic heat bath.
Qimiao Si reminded us about the two possible paths - local and spin density wave, from antiferromagnetism to paramagnetism. He suggested that recent work on Scandium doped UPd₃ by Wilson et al, which observes E/T scaling, is an example of a system where frustration drives the quantum critical point into a locally quantum critical point.	Two routes to quantum criticality: after Qimiao Si (see blog12 discussion)
Victor Khodel.	Victor Khodel told us that he has been working with Victor Yakovenko, on the flattening of single particle degrees of freedom (a k-space, rather than Z renormalization effect) as a model for quantum critical points. He remarked that they have found some interesting model solutions, which display Curie like susceptibilities and BCS like superconductivity - could this be a possible explanation for superconductivity in PuGaIn5?
Andrey Chubukov briefly described the work that he has carried out with Joerg Schmalian, on quark pairing by gluons. In a cold, dense quark fluid, the quarks are no longer confined, but gluons can pair the quarks to form a color superconductor. According to Andrey, the work began as an attempt to understand the exciting parallels between pairing of itinerant fermions near a ferromagnetic QCP and pairing of quarks due to the exchange by gluons. However, the work evolved into the attempt to understand whetheror not spin-fermion model breaks down once the interaction U becomes larger than the fermionic bandwidth. Andrey argued that he and Joerg found that at large interaction, a different, non-Eliashberg description become possible. In this description, the fermionic self- energy still predominantly depends on frequency, and vertex corrections remain at most O(1). He argued that in this situation, the system displays the precursors to pairing at temperatures of order hopping t, but the superfluid stiffness is much saller and scales as J ~ t²/U. He argued that these results are surprisingly similar to those of Mohit Randeria and his collaborators.	An event at RHIC - accelerator that produces high temperature quark-gluon plasmas.
Rech, Coleman, Parcollet, Zarand to be published. Phase diagram of 2ch Kondo model using Schwinger boson mean field theory. Entropy is color coded. Beneath the dashed region, bosons are paired. When TK/JH ~ 0.2, the competition between Heisenberg exchange and Kondo leads to a "Varma Jones" critical point, with a residual entropy.	Piers Coleman ended the discussion, and mentioned the work he has been doing with Jerome Rech, Olivier Parcollet and Gergely Zarand, trying to formulate a mean-field theory of the Kondo lattice that will incorporate both the Kondo effect, and local moment antiferromagnetism. He described how, by using the Parcollet Georges approach, of combining Schwinger bosons with a multi-channel Kondo lattice, where the number of channels K = 2S, it appears to be possible to correctly describe the Kondo effect and magnetism. One of the interesting features of this approach, is the appearance of a Fermi liquid phase with short-range magnetic correlations, with a gap for the disintegration of heavy electrons into holons and spinons. They think this gap closes at the quantum critical point.

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