Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session C37b: Theory of Quantum Critical and non-Fermi Liquid Behavior |
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Sponsoring Units: DCMP Chair: Andriy Nevidomskyy, Rice University Room: 384 |
Monday, March 13, 2017 2:30PM - 2:42PM |
C37b.00001: Superconductivity and bad metal behavior near a nematic quantum critical point Samuel Lederer, Yoni Schattner, Erez Berg, Steven Kivelson Using determinantal quantum Monte Carlo for systems of size up to $24\times 24$, we compute the properties of a lattice model with spin $\frac 1 2$ itinerant electrons tuned through a quantum phase transition to an Ising nematic phase. We find that the nematic fluctuations induce superconductivity with a broad dome in the superconducting $T_c$ enclosing the nematic quantum critical point. For temperatures above $T_c$, we see strikingly non-Fermi liquid behavior of the electron spectral properties -- including a ``nodal - anti nodal dichotomy'' reminiscent of that seen in high $T_c$ cuprates - and ``bad metal'' behavior of the conductivity. [Preview Abstract] |
Monday, March 13, 2017 2:42PM - 2:54PM |
C37b.00002: Finite temperature properties of non Fermi liquid state in the Anderson-Hubbard model Anamitra Mukherjee, Niravkumar D. Patel, Nitin Kaushal, Adriana Moreo, Elbio Dagotto We employ a recently developed many-body technique to study the half filled Anderson-Hubbard model at arbitrary Hubbard repulsion $U$ and disorder strength $V$ and at finite temperature. Using finite systems, we establish a quantum percolation threshold for the disorder induced metallization of Mott insulators, and map out the metallic regime as a function of temperature, disorder, and Hubbard repulsion. We thereby capture the continuous quantum phase transition between a Mott state and a non Fermi liquid metal. This metal shows scaling behavior of resistivity with temperature (as $T^\alpha$). We further find a continuum of values for the scaling exponent $\alpha$ in the metallic regime, as a function of disorder and interaction strength, in essence making it tunable. We discuss the properties of the disorder induced bad metal in the context of the 'charge glass' metallic state that can occur in the vicinity of a quantum critical point. [Preview Abstract] |
Monday, March 13, 2017 2:54PM - 3:06PM |
C37b.00003: Finite Conductivity without Momentum Relaxation and Violation of Charge Diffusion Bounds in Lifshitz Holography Brandon Langley, Philip Phillips We compute and analyze the optical conductivity at finite chemical potential in a holographic Lifshitz geometry using the Einstein-Dilaton-Maxwell action. From the exact expression for the DC conductivity, we find that for a dynamical exponent $z\neq 1$, the conductivity is finite, despite the system exhibiting translational invariance. This indicates that interactions alone are sufficient for generating finite conductivities even in systems without momentum relaxation. We confirm our result by computing the conductivity numerically and find it does not take a Drude form, indiciating our model represents an incoherent metal. Our exact computation of the charge diffusivity reveals it is possible to violate the Hartnoll diffusivity bound, where we use the butterfly velocity as the proposed characteristic velocity in our model. [Preview Abstract] |
Monday, March 13, 2017 3:06PM - 3:18PM |
C37b.00004: Level Statistics of the Sachdev-Ye-Kitaev Model Yi-Zhuang You, Andreas Ludwig, Cenke Xu We consider the Sachdev-Ye-Kitaev (SYK) model as an effective theory arising at the zero-dimensional boundary of a many-body localized, Fermionic symmetry protected topological (SPT) phase in one spatial dimension. The Fermions at the boundary are always fully interacting. We find that the boundary is thermalized and investigate how its boundary anomaly, dictated by the bulk SPT order, is encoded in the quantum chaotic eigenspectrum of the SYK model. We show that depending on the SPT symmetry class, the boundary many-body level statistics cycle in a systematic manner through those of the three different Wigner-Dyson random matrix ensembles with a periodicity in the topological index that matches the interaction-reduced classification of the bulk SPT states. We consider all three symmetry classes BDI, AIII, and CII, whose SPT phases are classified in one spatial dimension by $\mathbb{Z}$ in the absence of interactions. For symmetry class BDI, we derive the eight-fold periodicity of the Wigner-Dyson statistics by using Clifford algebras. [Preview Abstract] |
Monday, March 13, 2017 3:18PM - 3:30PM |
C37b.00005: Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models Yingfei Gu, Xiao-Liang Qi, Douglas Stanford The Sachdev-Ye-Kitaev model is a $(0+1)$-dimensional model describing Majorana fermions or complex fermions with random interactions. This model has various interesting properties such as approximate local criticality (power law correlation in time), zero temperature entropy, and quantum chaos. In this article, we propose a higher dimensional generalization of the Sachdev-Ye-Kitaev model, which is a lattice model with $N$ Majorana fermions at each site and random interactions between them. Our model can be defined on arbitrary lattices in arbitrary spatial dimensions. In the large $N$ limit, the higher dimensional model preserves many properties of the Sachdev-Ye-Kitaev model such as local criticality in two-point functions, zero temperature entropy and chaos measured by the out-of-time-ordered correlation functions. In addition, we obtain new properties unique to higher dimensions such as diffusive energy transport and a ``butterfly velocity'' describing the propagation of chaos in space. We mainly present results for a $(1+1)$-dimensional example, and discuss the general case near the end. [Preview Abstract] |
Monday, March 13, 2017 3:30PM - 3:42PM |
C37b.00006: Quantum chaos on a critical Fermi surface Aavishkar Patel, Subir Sachdev We compute parameters characterizing many-body quantum chaos for a critical Fermi surface without quasiparticle excitations. We examine a theory of $N$ species of fermions at non-zero density coupled to a $U(1)$ gauge field in two spatial dimensions, and determine the Lyapunov rate and the butterfly velocity in an extended random-phase approximation. The thermal diffusivity is found to be universally related to these chaos parameters i.e. the relationship is independent of $N$, the gauge coupling constant, the Fermi velocity, the Fermi surface curvature, and high energy details. [Preview Abstract] |
Monday, March 13, 2017 3:42PM - 3:54PM |
C37b.00007: Solvable model for a dynamical quantum phase transition from fast to slow scrambling Ehud Altman, Sumilan Banerjee We propose an extension of the Sachdev-Ye-Kitaev (SYK) model that exhibits a quantum phase transition from the previously identified non-Fermi liquid (NFL) fixed point to a Fermi liquid like state, while still allowing an exact solution in a suitable large $N$ limit. The extended model involves coupling the interacting $N$-site SYK model to a new set of $pN$ peripheral sites with only quadratic hopping terms between them. The conformal fixed point of the SYK model remains a stable low energy phase below a critical ratio of peripheral sites $p_c$ that depends on the fermion filling $n$. The scrambling dynamics throughout the non-Fermi liquid phase is characterized by a universal Lyapunov exponent $\lambda\to 2\pi T$ in the low temperature limit, however the temperature scale marking the crossover to the conformal regime vanishes continuously at the critical point $p_c$. The residual entropy at $T\to 0$, non zero in the NFL, also vanishes continuously at the critical point. For $p>p_c$ the quadratic sites effectively screen the SYK dynamics, leading to a quadratic fixed point in the low temperature and frequency limit. The interactions have a perturbative effect in this regime leading to scrambling with Lyapunov exponent $\lambda\propto T^2$. [Preview Abstract] |
Monday, March 13, 2017 3:54PM - 4:06PM |
C37b.00008: Thermoelectric transport in SYK and holographic models of disordered non-Fermi liquids Wenbo Fu, Richard Davison, Yingfei Gu, Jensen Kristan, Subir Sachdev We describe charged Sachdev-Ye-Kitaev (SYK) models, which contain complex fermions with q/2-body, Gaussian-random, all-to-all interactions. A low-energy effective action is derived: it is described by a re-parameterization field, representing energy fluctuations, and a phase field, representing charge fluctuations. We compute thermoelectric transport properties, and show that they match perfectly with holographic results obtained from black holes with AdS2 horizons and momentum dissipation. [Preview Abstract] |
Monday, March 13, 2017 4:06PM - 4:18PM |
C37b.00009: The holographic dual of thermoelectric transport in SYK models Richard Davison, Wenbo Fu, Yingfei Gu, Kristan Jensen, Subir Sachdev Sachdev-Ye-Kitaev (SYK) models are models of fermions with infinite-ranged, random interactions. These models exhibit compressible, metallic states with no quasiparticle excitations. I will show that relations between the thermoelectric conductivities of these states are quantitatively the same as those found by studying charged black holes with AdS$_2$ geometries near their event horizon. This is evidence that, at low energies, SYK models have a dual, holographic description as a theory of gravity. [Preview Abstract] |
Monday, March 13, 2017 4:18PM - 4:30PM |
C37b.00010: Spatial structure of entanglement in a system near a Kondo destruction quantum critical point Chris Wagner, Tathagata Chowdhurry, Kevin Ingersent, Jedediah Pixley We use entanglement entropy as a probe of the ground state of the pseudogap Kondo model near a quantum critical point (QCP) that separates a Kondo-screened phase (reached for impurity-band exchange couplings $J>J_c$) from a Kondo-destroyed or local-moment phase ($J < J_c$). The impurity contribution to the entanglement entropy between a region of radius $R$ around the magnetic impurity and the rest of the semimetallic host reveals a characteristic length scale $R^*$ that distinguishes a regime $R\ll R^*$ of maximal critical entanglement from one $R\gg R^*$ of weaker entanglement. In contrast to the conventional case of a metallic host, entanglement in the Kondo phase remains nonzero for $R\gg R^*$, suggesting that the Kondo screening cloud is infinite. In the local-moment phase, the strong entanglement for $R\ll R^*$ evidences a dynamical Kondo effect, but the entanglement decreases toward zero for $R \gg R^*$. Within each phase, the impurity entanglement entropy computed via the numerical renormalization group is well described as a universal function of $R/R^*$. The value of $R^*$ diverges on approach to the QCP like $|J-J_c|^{-\nu}$, where $\nu$ is the correlation length exponent, leading to maximal entanglement extending throughout the entire system. [Preview Abstract] |
Monday, March 13, 2017 4:30PM - 4:42PM |
C37b.00011: Particle-vortex symmetric liquid Michael Mulligan The magnetic field-tuned superconductor-insulator transition in disordered films is a fascinating example of a quantum phase transition. A useful framework for its description involves "dirty" Cooper-pair bosons that undergo a continuous order-disorder transition. Particle-vortex duality implies an alternative description in terms of field-induced vortices that likewise undergo a second-order transition. A recent experiment by Breznay et al. indicates that the transition is "self-dual": this implies the Cooper-pair bosons and field-induced vortices have identical dynamics at the transition. How can this be? Cooper-pair bosons carry electrical charge, while vortices are neutral. In this talk, I'll describe an effective theory that is manifestly self-dual and discuss a few of its implications, which include a prediction of approximately equal (diagonal) thermopower and Nernst signal at the transition with a deviation parameterized by the measured electrical Hall effect. In addition, I'll discuss how this theory is related to recent theoretical progress in our understanding of "bosonization" in 2+1 dimensions and new ideas for the theoretical description of the half-filled Landau level of the two-dimensional electron gas. [Preview Abstract] |
Monday, March 13, 2017 4:42PM - 4:54PM |
C37b.00012: Berry Phase in in Fermi and Non-Fermi Liquids Jing-Yuan Chen In the recent year it has been realized that Berry phase is a unified theme underlying a lot of interesting physics, such as anomalous Hall effect, chiral anomaly transport etc. However, much of the discussions of Berry phase were based on the picture of non-interacting single fermions. We want to justify which Berry phase properties survive upon the inclusion of interactions, and whether there are new effects arising from interactions. We first consider Fermi liquids and show, from quantum field theory, that Landau's low energy kinetic formalism can be extended to incorporate Berry phase. Next we consider certain non-Fermi liquids and show certain transport properties are given purely by the Berry phase and are not mixed up by the mysterious nature of excitations in non-Fermi liquids. [Preview Abstract] |
Monday, March 13, 2017 4:54PM - 5:06PM |
C37b.00013: Controlling Feynman diagrammatic expansions: physical nature of the pseudo gap in the two-dimensional Hubbard model Wu Wei, Michel Ferrero, Antoine Georges, Evgeny Kozik We introduce a method for summing Feynman's perturbation series based on diagrammatic Monte Carlo that significantly improves its convergence properties. This allows us to investigate in a controllable manner the pseudogap regime of the Hubbard model and to study the nodal/antinodal dichotomy at low doping and intermediate coupling. Marked differences from the weak coupling scenario are manifest, such as a higher degree of incoherence at the antinodes than at the `hot spots'. Our results show that the pseudogap and reduction of quasiparticle coherence at the antinode is due to antiferromagnetic spin correlations centered around the commensurate $(\pi,\pi)$ wavevector. In contrast, the dominant source of scattering at the node is associated with incommensurate momentum transfer. Umklapp scattering is found to play a key role in the nodal/antinodal dichotomy. [Preview Abstract] |
Monday, March 13, 2017 5:06PM - 5:18PM |
C37b.00014: Linearly dispersing spinons at the deconfined quantum critical point Hidemaro Suwa, Arnab Sen, Anders Sandvik We have studied the level structure of excitations at the "deconfined" critical point separating antiferromagnetic and valence-bond-solid phases in two-dimensional quantum spin systems using the $J$-$Q$ model as an example. Energy gaps in different spin ($S$) and momentum (${\bf k}$) sectors are extracted from imaginary-time correlation functions obtained in quantum Monte Carlo simulations. We find strong quantitative evidence for deconfined linearly dispersing spinons with gapless points at ${\bf k}=(0,0)$, $(\pi,0)$, $(0,\pi)$, and $(\pi,\pi)$, as inferred from two-spinon excitations ($S=0$ and $S=1$ states) around these points. We also observe a duality between singlet and triplet excitations at the critical point and inside the ordered phases, in support of an enhanced symmetry, possibly SO(5). [Preview Abstract] |
Monday, March 13, 2017 5:18PM - 5:30PM |
C37b.00015: Effect of disorder on the critical behavior of interacting 3D Dirac and Weyl semimetals Jose Gonzalez We investigate the effect of disorder on the critical behavior of 3D Dirac and Weyl semimetals with long-range Coulomb interaction. We show that short-range disorder potentials (correlated disorder) do not destabilize the non-Fermi liquid phase of these systems at strong interaction strength, but they induce in general a decrease of the Fermi velocity that competes with a significant screening of the interactions. As a consequence of that, we find a line of unstable fixed points (at weak interaction strength) where the effective couplings of the disorder and the interaction remain scale invariant. At one side of the line, the system flows to a regime with regular Fermi liquid behavior. At the other side, the disorder plays the dominant role to drive the system towards a phase with vanishing quasiparticle weight. At intermediate interaction strength, screening effects always prevail, stabilizing a semi-metallic phase with renormalized quasiparticle parameters. [Preview Abstract] |
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