KITP - 2

Quantum Phase Transitions

Week 2. Conference.
18-21 January, 2004

Bloggers:   Piers Coleman, assisted by Andrey Chubukov, Dirk Morr, Hilbert von Lohneysen, Vladimir Dobrosavljevic and Thomas Vojta.

The conference was designed to kick-start the workshop, raising questions and introducing new experimental and theoretical material that will stimulate the months ahead. About 100 participants came, some from as far afield as Australia. We heard a broad range of fascinating talks, ranging from quantum phase transitions in oxides and intermetallics, to Bose Einstein condensates and finally, two beautiful talks speculating on possible links with particle and String theory. All of the talks and slides for the conference are available online. Our blog page this week provides an opinionated guide to the talks and their contents, plus a little insight into the discussions that also took place.

The program of the conference was designed to give a large amount of time to discussion, following the "Frauenfelder" model - this meant that regular talks were officially only 15 minutes long, with 25 minutes for discussion. Longer review talks were allowed 30 minutes, and 10 minutes for discussion. Discussion was lively, yet largely friendly. We were blessed by beautiful weather and thanked our lucky stars that we had not scheduled the meeting on the previous week when Ventura highway was closed.

The KITP provided a marvellous venue for this small meeting. All coffee breaks and meals were held under awnings in the shady, central courtyard. Tables were laid out, and physicists were often found in lively discussion and calculation. The official conference started on Tuesday, after Martin Luther King day.

Tuesday, 18th.      Intermetallics
Wednesday, 19th. Cuprates
Thursday, 20th.    Ferromagnets and transition metals
Friday, 21st .        Atom Traps, 2D Metal Insulator and links with field theory.

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Tuesday, 18th. Intermetallics
Catherine Pépin* (SPhT, CEA-Saclay)	Quantum Critically in Heavy Fermion compounds: interpay of Kondo screening and magnetic fluctuations
[Slides][Aud][Cam]	Overview, with extensive references, of the strange properties of heavy electron metals near a quantum critical point, raising the following questions: What is the right starting model? Local versus intinerant criticality? Is there a sudden change Fermi surface volume at a QCP? Is there a new kind of excitation at a QCP? Pepin outlined the various new scenarios for the physics at the QCP, including the ideas of fermion condensation, local quantum criticality and deconfinement.
Sachdev questioned the meaning of (4), esp in the light of the change in the unit cell of the crystal that accompanies the quantum critical point.
Philipp Gegenwart (Univ. St. Andrews)	Magnetic properties of the Heavy Fermion state in YbRh₂Si₂
[Slides][Aud][Cam]	Strong Ferromagnetic spin fluctuations appear to develop in the vicinity of the field-induced quantum critical point of YbRh₂Si₂ . 4f eletrons localize at 10T but without any sudden metamagnetic rise in magnetization. A big open mysteries, is why the ratio is constant.
Paul Canfield (Iowa State Univ.)	Field Induced Quantum Critical Point in YbAgGe
[Slides][Aud][Cam]	YbAgGe has a very different crystal structure to YbRh₂Si₂ , yet shows many similar features.This material can be made in large single crystals. Like YbRh₂Si₂ , the Hall resistance shows a peak that appears to sharpen at lower temperatures and join with the magnetic quantum critical point. What does this mean? Is there a quantum critical point or line?
Subir Sachdev (Yale Univ.)	Quantum phase transitions out of the heavy Fermi liquid
[Slides][Aud][Cam]	Three scenarios with relevance to quantum phase transitions in heavy electron systems were presented. Bose-Fermi mixtures, with two or one Luttinger rule, depending on whether bosons are condensed. Quantum phase transition between a spin liquid and a heavy electron fluid. Deconfined criticality, in which there are two diverging correlation lengths, one dominating the critical point, one dominating the eventual ordered phase.
Kevin Ingersent (Univ. Florida)	Quantum criticality in the Bose-Fermi Kondo model
[Slides][Aud][Cam]	Two applications of the Bose-Fermi model were introduced: To a noisy quantum dot To the locally quantum critical model of a QCP The solution of this model using a Wilson numerical RG, in which the fermions are included in the calculation, explicitly demonstrates E/T scaling and destruction of Kondo resonance. One of the open questions that this method hopes to resolve, is whether there is a locally quantum critical point within EDMFT, or whether, as some believe, this critical point is pre-empted by a first order phase transition. This is not a question that can be fully resolved with Monte Carlo methods. Future use of these Wilson RG methods on the Bose-Kondo model, with full EDMFT self-consistency will be used to resolve this important issue.
Thomas Vojta* (Univ. Missouri-Rolla)	Quantum phase transition and disorder: rare regions, Griffiths effects, and smearing
[Slides][Aud][Cam]	Effects of impurities near quantum phase transition were discussed with emphasis on the physics of rare disordered configurations - the "quantum Griffiths phase". These effects often lead to new thermodynamic singularities, not only at the quantum critical point, but also in an exteded region within the quantum paramagnetic phase. Arguments were presented, demonstrating that in itinerant systems such Griffiths phases are very sensitive to dissipative processes due to Landau damping. As a result, sufficiently large droplets become overdamped and freeze out, making them susceptible to ordering by infinitesimally weak inter-droplet interactions. This mechanism is predicted to result in a qualitative modification of the quantum critical behavior in itinerant systems, which is expected to be "rounded" by any finite amount of disorder.
Vladimir Dobrosavljevic (FSU)	Non-Ohmic dissipation in electronic Griffiths phases
[Slides][Aud][Cam]	In the first part of his talk, Vlad contrasted several mechanisms by which disorder can lead to non-Fermi liquid behavior, notably Kondo disorder, electronic Griffiths phases associated with a metal-insulator transition, and magnetic Griffiths phases associated with magnetic quantum phase transitions. He pointed out that these mechanisms can lead to very similar phenomenology in the usual observables such as specific heat or magnetic susceptibility. Therefore, great care has to be taken in associating experimental observations to one of the above scenarios. In the second part of his talk, Vlad focused on the role of interactions between the rare events in an electronic Griffiths phase near a metal-insulator transition. He pointed out that RKKY interactions have to be taken into account for those spins whose Kondo temperature is small due to disorder fluctuations. These long-range interactions produce a strong non-ohmic damping which can destroy the Kondo effect. A self-consistent DMFT-based calculation gives a marginal Fermi liquid solution with a universal distribution of Kondo temperatures P(T_K) \sim T_K^{-1/2} and \chi(T) \sim log(1/T). This marginal Fermi liquid phase can be understood as precursor of a spin glass phase which will show up at very low temperatures.
Greg Stewart* (Univ. Florida)	Experimental Status Report on Disordered QPTs: Still Challenging Theory
[Slides][Aud][Cam]	Greg presented results on three heavy-fermion compounds (Ce,La)RhIn5, (Ce,Th)RhSb, and U(Cu,Ni)5, primarily specific heat and magnetization. He presented fits to the Castro Neto version of the Griffiths model. While some features of the data can be accounted for qualitatively in his model, a rough quantitative estimate performed during the talk indicated that the observed specific heat contributions are too large to be accounted for by tunneling of "rare ordered regions" of the Griffiths model. Independent of that model, the issue of a controlled change of the disorder is of course of primary importance and in my view experiments should look for and focus on systems where a control of the degree of disorder is possible. (HvL)
Tom Rosenbaum (Univ. Chicago)	Probing Quantum Phase Transitions and Domain Dynamics with the Hall Effect
[Slides][Aud][Cam]	Tom Rosenbaum described the use of the Hall effect to gain insight into the evolution of the Fermi surface at the antiferromagnetic quantum critical point of chrome vanadium. Interesting points: Whereas the Hall constant and Neel temperature are governed by exponent 0.5 1/R_H~ (P_c-P)^1/2 T_N~ (P_c-P)^1/2 the Residual resistance has exponent 0.68 rho~ (P_c-P)^0.68 What is the origin of these two exponents? The T³resistance is due to phonons. (no small angle scattering by symmetry) The Hall constant exhibits temperature hysteresis - indicative of domain formation.
Weds 19th. Cuprates
Brad Marston* (Brown Univ.)	High-T_c Superconductivity: Known Knowns and Unknowns
[Slides][Aud][Cam]	This is a review talk on quantum criticality in the cuprates. Instead of listing specific arguments for and against quantum critical point beneath the superconducting dome, Brad addressed the question whether layered cuprates would still stand out among other layered materials, if T_c were not so high. He discussed similarities between high T_c cuprates and three other classes of layered materials -- a quasi-1D triangular antiferromagnet, Cs₂CuCl₄, which displays spin liquid behavior at intermediate temperatures with spinon-like excitations, an organic superconductor k-(BEDT-TTF)₂Cu[N(ClN)₂]Cl, which displays a pseudogap behavior and anisoteropic superconductivity, a two-leg ladder compound Sr1₄Cu₂₄O₄₁ which displays spinon-like excitations and CDW ordering.
Dirk van der Marel (Univ. Geneva)	Quantum critical behavior in a high-T_c superconductor
[Slides][Aud][Cam]	Dirk presented the ellipsometry data for both real and imaginary parts of the optical conductivity σ (ω). He argued that in a wide range of frequencies, the conductivity follows σ ^ -γ behavior, with γ ~ 0.6-0.7. He contrasted this with the low-frequency form of the conductivity which scales linearly with either 1/ω or 1/T.
Christos Panagopoulos (Cambridge)	Short range order and quantum glassiness in the high-T_c cuprates
[Slides][Aud][Cam]	In this talk, Christos argued for the existence of the quantum critical point near optimal doping. His arguments are based on the observations of the spin-freezing transition in the experiments on muon relaxation rate. He argued below the transition, the system develops a spin-glass order, which can co-exist with superconductivity.
Chandra Varma (UC Riverside)	The critical fluctuations at the Quantum critical point in the Cuprates
[Slides][Aud][Cam]	Chandra argued for the phase diagram with the quantum-critical pointnear optimal doping and marginal Fermi liquid (MFL) behavior in thecritical region. He presented B1g Raman data in YBCO which show thesaturation of the Raman intensity at high frequencies, and ω/Tscaling at low frequencies. He argued that one can extract from the data the bosonic mode which gives rise to MFL behavior in the intermediate regime. He also argued that three-band mode is necessary to obtain MFL behavior theoretically.
Patrick Lee (MIT)	Who and where is the QCP in cuprates?
[Slides][Aud][Cam]	Patrick split his talk into two parts. In the first, he argued against a quantum-critical point under the superconducting dome. He argued that \omega/T scaling is not necessary a signature of quantum criticality. He described in some detail the SU(2) formulation of the gauge theory and discussed possible signatures of deconfined spinons in the spin-liquid phase (which is the pseudogap phase in his scenario). In the second part of the talk, he discussed possible spin-liquid phases in Mott insulators on triangular and honeycomb lattices.
Thursday, 20th. Ferromagnets and transition metals
Andrew Schofield* (Univ. Birmingham)	Ferromagnetic quantum criticality: an overview
[Slides][Aud][Cam]	Andy presented a review on ferromagnetic quantum criticality. He briefly reviewed the Hertz-Millis theory, listed its predictions, and discussed its validity on theoretical grounds, and with respect to the experimental data. He argued that experimentally, ferromagnetic transition is likely the first order in all known materials.He then considered in some detail the system behavior near a metamagnetic quantum critical endpoint. He argued that Hertz-Millis theory works reasonably well for this transition, but very recent data show that the behavior very near QCP is more complex than previously thought. He argued that this behavior may be a signature of a new phase near the quantum critical endpoint.
Meigan Aronson (Univ. Michigan)	Quantum Critical Point in the Itinerant Ferromagnets Zr1-xNbxZn2
[Slides][Aud][Cam]	Meigan presented the data for Zr_{1-x} Nb_x Zn_2 in which a ferromagnetic transition temperature is suppressed by $Nb$ and is driven to zero at x=0.085. She argued that near this new ferromagnetic quantum-critical point, a 3D Stoner theory works well, however anomalous power-law behavior of the spin susceptibility persists in some range of doping above critical x.
Christoph Bergemann (Cambridge)	Quantum Critically and Fermi Surface Topology Transitions
[Slides][Aud][Cam]	In this talk, Christophe discussed the relation between quantum critical point and the change in the Fermi surface topology. He presented the data on Hall constant in $Sr_2 RuO_4$ doped by $La$ and argued that the Hall constant changes the sign long before the system reaches a critical $la$ concentration at which the Fermi surface changes from electron-like to hole-like. He also considered $CeRu_2Si_2$ and argued that in this compound, there exists a field-driven change of the Fermi surface topology, but the system does not seem to display quantum-critical behavior at the critical field.
Dietrich Belitz (Univ. Oregon)	Ferromagnetic Quantum Critical: Breakdown of the Perturbative Renormalization Group
[Slides][Aud][Cam]	In his talk, Dietrich discussed in detail how the perturbative renormalization group treatment breaks down near a quantum phase transition in a dirty itinerant ferromagnet. He considered $\phi^4$ theory coupled to a diffusive mode and demonstrated that one can write a closed set of two equations for the propagators of the $\phi$ field and the diffusive mode. He analyzed the structure of the RG equations and demonstrated that the loop expansion breaks down as, at the two-loop order, a coupling constant which originally thought to be totally irrelevant, appears under the logarithm and thus affects the structure of the RG equations for relevant couplings. He presented a highly non-trivial expression for the temperature dependence of the spin correlation length near the ferromagnetic quantum transition.
Dimitri Maslov (Univ. Florida)	Singular corrections to the Fermi-liquid behavior: 1D physics in higher dimensions
[Slides][Aud][Cam]	In his talk, Dmitrii reviewed recent works on non-analytic and singular corrections to the Fermi liquid. He argued that in $d\leq 3$, the subleading terms in the expansion of the spin susceptibility and the specific heat in temperature are universal, non-analytic, and originate from 1D backscattering processes -- the same processes that destroy Fermi liquid in 1D. He discusses in some detail the physical origin of this behavior. He also argued that forward scattering does not contribute to thermodynamics, but in $D=2$ leads to a non-analyticity in the spectral function of a Fermi liquid near the mass shell. He discussed how these non-analytic corrections modify the system behavior near a ferromagnetic quantum critical point.
John Sarrao* (LANL)	Tuning unconventional superconductivity in "115" materials
[Slides][Aud][Cam]	This talk briefly reviewed the properties of the 115 materials, CeMIn5 with M=Rh, Ir, Co. It then reported on the properties of a new member of this family, PuCoGa5, with a superconducting Tc=18.5K. NMR measurements indicate that PuCoGa5 possesses line nodes and is likely a d-wave superconductor. Tc for the 115 materials exhibits a linear dependence on c/a, where c (a) is the out-of-plane (in-plane) lattice constant. In doped CeCoIn5-xSnx the quantum critical point appers glued to the upper critical field and does not reveal any hidden antiferromagnetism. It was argued that Rh1-xIrxIn5 possesses a crossover from spin-fluctuation to charge-fluctuation mediated superconductivity.
Christian Pfleiderer (Univ. Karlsruhe)	Partial Order in the NFL Phase of MnSi
[Slides][Aud][Cam]	At low pressure, MnSi possess a spiral ferromagnetic order with an ordering wavevector along the (111) direction. Above a critical pressure, pcï‚»14.6 kbar, this order disappears, and MnSi exhibits non-Fermi-liquid (NFL) behavior, such as a resistivity exponent of 3/2. In this talk, recent INS experiments in the NFL region of MnSi were presented. It was argued that the ordered ferromagnetic moment is not destroyed at pc, but that the ordering wavevector is smeared out in a direction perpendicular to the (111)-direction. It was shown that by applying a magnetic field, the ordered moment can again be aligned into the (111)-direction.
Nick Curro (LANL)	The Discovery of Scaling in the Emergent Heavy Electron Component in a Kondo Lattice
[Slides][Aud][Cam]	In many heavy electron systems, the linear relationship between the Knight-shift and the local susceptibility breaks down (this is know as the Knight shift anomaly). In this talk, it was proposed that this anomaly can be understood in terms of a two-fluid model, in which a â€œheavy-fermionâ€� component of the susceptibility emerges below a characteristic temperature, T. leading to a Knight-shift, Kcf, Support for this idea comes from a plot of Kcf (T)/ Kcf (0) as a function of T/ T which exhibits a scaling behavior for many heavy-electron systems. Finally, it was shown that PuCoGa5 possess an NMR relaxation rate that is similar to that of the high-temperature superconductors, supporting the idea of similarly strong AFM fluctuations.
Indranil Paul (CEA Saclay)	Quantum Correction to Conductivity Close to Ferromagnetic Quantum Critical Point in Two Dimensions: Ballistic Regime [Slides][Aud][Cam]
[Slides][Aud][Cam]	This talk addressed the questions whether strong magnetic fluctuations near a ferromagnetic quantum critical point (in 2D) can change the low-temperature behavior of the conductivity from that of a conventional Fermi liquid (FL). Corrections to the conductivity arise from quantum interference processes where an electron is scattered by an impurity and the Friedel oscillations created by the impurity. For a conventional FL, this leads to a logarithmic temperature correction in the conductivity. Using a spin-fermion model, it was shown that in the presence of ferromagnetic fluctuations, elastic scattering processes dominate inelastic ones. In particular, the former give rise to a T1/3 contribution to the conductivity, while the latter scales as T4/3.
Friday 21st. Atom Traps, 2D Electron Gas and link with Field Theory
Hans Peter Buchler (Univ. Innsbruck)	Design and realization of exotic quantum phases in atomic gases
[Slides][Aud][Cam]	This talk briefly reviewed the physical principles for creating optical lattices using atomic gases. It was then shown (a) that certain optical lattices can be described by Bose-Hubbard Hamiltonians, and (b) that these systems should exhibit a transition from a superfluid to Mott Insulator. It was demonstrated how a bosonic Ring exchange can emerge in optical lattices. By changing the detuning, such an exchange term can give rise to a crossover from a superfluid to a ground state in which the bosonic atoms from molecules. Interesting points to emerge: Using lasers it is now possible to flatten out the parabolic potential, so that finite size effects of the potential can be removed. It is not yet clear, to what extent atom traps represent a truly equilibrium distribution of particles - the shoulders on the figure to the left may reflect a non-equilibrium component. Fermions in optical lattices are on the way. One of the challenges to theorists, is to think of new ways to extract spectroscopic information from the tools the atom trappers are developing.
Sergey Kravchenko (Northeastern Univ.)	Critical behavior of the Paul spin susceptibility near the 2D metal-insulator transition
[Slides][Aud][Cam]	In clean systems, a practically universal metal-insulator transition occurs when the electron density is changed. This talk addressed the question whether this transition is a true phase transition, or a crossover phenomenon. By measuring the thermodynamic magnetization of the sample, it was shown that a spontaneous polarization occurs at an electron density, nï�£, which is close to that at of the MI transition. It was also found that a jump in the density of states coincides with the onset of the full spin polarization, and that the spin polarization diverges at nï�£. No evidence for an increase of the g-factor at nï�£ was found, such that the divergent susceptibility likely arises from a divergence in the effective mass.
Joe Polchinski* (KITP)	Quantum Criticality in String/M Theory
[Aud][Cam]	This talk discussed the duality of an N=4, D=4 supersymmetric gauge theory and string theory, the AdS/CFT duality. The studies of black-hole in string theory are based on an adiabatic continuation between D-branes and black branes. Their low-energy theories are the CFT and AdS theory, respectively. Thus, the strongly coupled dynamics of the gauge theory can be obtained within a string theory. A dictionary for the translation of physical properties of the string theory into the gauge theory was discussed.
Scott Thomas (Stanford)	Emergent Supersymmetry
[Slides][Aud][Cam]	This talk gave a short introduction into supersymmetric theories and their ingredients, and reviewed some possible applications of supersymmetry in condensed matter systems. In particular, Scott introduced the idea that supersymmetry can emerge as a longwavelength property. He illustrated this with N=1 and N=2 SUSY in D=3 for which the RG-flow equations, the critical exponents and the RG-flow diagram were derived. It was argued that superconformal theories can emerge in D=3.
DISCUSSION	To Do or Not To Do - Integrating out the Fermions in Quantum Critical Models
[Aud][Cam]	The assembly discussed the current status of our understanding of quantum critical points. Paul Canfield described the phase diagram of YbAgGe and the things he would like some theoretical guidance about. A consensus developed that for the field-induced quantum critical point, and - according to Chubukov, also in the spiral antiferromagnet, one can "integrate out the fermions" to derive a Hertz theory. Unfortunately, this theory doesn't work for CeCu6Au. What are the missing degrees of freedom in the bad-actor heavy electron quantum critical points? Does the physics of local moments play a key role? The discussants thought it might.