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arXiv:1612.00849 · Physical review. B./Physical review. B

Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography

Richard A. Davison, Wenbo Fu, Antoine Georges, Yingfei Gu, Kristan Jensen, Subir Sachdev A

Published Apr 18, 2017• 435 citations
arXivHTMLPDF

Abstract

Essentially all high temperature superconductors display a ``strange metal'' regime above their critical temperatures, where electrical and thermal transport cannot be explained within the traditional Fermi liquid paradigm of quasiparticle excitations. This paper focuses on the first, and newly discovered, solvable theory of a disordered metal without quasiparticle excitations, obtained by extending the Sachdev-Ye-Kitaev (SYK) models to finite spatial dimensions. The complete thermoelectric conductivity matrix is computed, and a surprising exact relation is found between the Seebeck coefficient and the derivative of the thermodynamic entropy with respect to the density. These computations are then compared with holographic theories which map strange metals onto black holes in theories of quantum gravity with one extra spatial dimension.

DOI
10.1103/physrevb.95.155131

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Essentially all high temperature superconductors display a ``strange metal'' regime above their critical temperatures, where electrical and thermal transport cannot be explained within the traditional Fermi liquid paradigm of quasiparticle excitations. This paper focuses on the first, and newly discovered, solvable theory of a disordered metal without quasiparticle excitations, obtained by extending the Sachdev-Ye-Kitaev (SYK) models to finite spatial dimensions. The complete thermoelectric conductivity matrix is computed, and a surprising exact relation is found between the Seebeck coefficient and the derivative of the thermodynamic entropy with respect to the density. These computations are then compared with holographic theories which map strange metals onto black holes in theories of quantum gravity with one extra spatial dimension.
This thesis is devoted to the study of Sachdev-Ye-Kitaev (SYK) models, which describe matter without quasiparticles. The SYK model is an exactly solvable model that is hoped to bring insights into the understanding of strongly correlated materials.\nThe main part discusses different aspects of SYK models. Chapter 2 presents numerical studies of the SYK models, shows its non-Fermi liquid nature and verifies the analytical predictions on two-point function and thermal entropies. Chapter 3 considers the thermodynamic and transport properties of the complex SYK models in higher dimensional generalizations, we show some universal relations obtained from SYK models which are consistent with holographic theories. Chapter 4 discusses a supersymmetric generalization of the SYK model. We show a different a scaling from the normal SYK model both analytically and numerically. We also discuss a different origin of the extensive zero temperature entropy in mathcalN=2\\mathcal{N}=2mathcalN=2 theory. Chapter 5 considers a continuous set of boson-fermion SYK models with a tunable low-energy scaling dimension. From the explicit computation of out of time ordered correlators, we find the theory is less chaotic in the free fermion limit. Chapter 6 describes the phases of a solvable ttt-JJJ model of electrons with an SYK-like form. We find a mathbbZ2\\mathbb{Z}_2mathbbZ2​ fractionalization picture where the deconfined phase is similar to the pseudo gap regime of underdoped cuprates, while the `quasi-Higgs' phase is similar to the metallic phase of overdoped cuprates.
Models for strongly interacting fermions in disordered clusters forming an array, with electron hopping between sites, reproduce the linear dependence on temperature of the resistivity, typical of the strange metal phase of high temperature superconducting materials [extended Sachdev-Ye-Kitaev (SYK) models]. We identify the low energy collective excitations as neutral energy excitations, diffusing in the lattice of the thermalized non-Fermi liquid phase. However, the diffusion is heavily hindered by coupling to the pseudo-Goldstone modes of the conformal broken symmetry SYK phase, which are local in space. The imaginary time evolution of the extended model in the strong interaction and 1/N1/N1/N expansion limit is presented in the incoherent nonchaotic regime. On the other hand, a Fermi electronic liquid at low energy becomes marginal when perturbed by the SYK dots. A critical temperature for superconductivity is derived, which is not BCS-like, in case the collective excitations are assumed to mediate an attractive Cooper pairing.
This dissertation is a study of various aspects of metals with strong interactions between electrons, with a particular emphasis on the problem of charge transport through them. We consider the physics of clean or weakly-disordered metals near some quantum critical points, and highlight novel transport regimes that could be relevant to experiments. We then develop a variety of exactly-solvable lattice models of strongly interacting non-Fermi liquid metals using novel non-perturbative techniques based on the Sachdev-Ye-Kitaev models, and relate their physics to that of the ubiquitous “strange metal” normal state of most correlated-electron superconductors, providing controlled theoretical insight into the possible mechanisms behind it. Finally, we use ideas from the field of quantum chaos to study mathematical quantities that can provide evidence for the existence of quasiparticles (or the lack thereof) in quantum many-body systems, in the context of metals with correlated electrons.
The Sachdev-Ye-Kitaev (SYK) model is a solvable model of a many-body quantum system that has stimulated interest in both condensed matter physics and quantum gravity. This review focuses on the insights provided by the SYK model, which has no quasiparticle excitations, into the physics of Planckian non-Fermi-liquid metals. This is discussed for a range of strongly correlated models and in relation to experiments on strongly correlated materials. Also included is a discussion of recent developments regarding the connections between the SYK model and the quantum theory of black holes.
Energy transport in quantum many-body systems with well defined quasiparticles has recently attracted interest across different fields, including out of equilibrium conformal field theories, one dimensional quantum lattice models and holographic matter. Here we study energy transport between \emph{strange quantum baths} without quasiparticles, made by two Sachdev-Ye-Kitaev (SYK) models at temperatures TL≠TRT_L\neq T_RTL​=TR​ and connected by a Fermi-Liquid system. We obtain an exact expression for the nonequilibrium energy current, valid in the limit of large bath and system size and for any system-bath coupling VVV. We show that the peculiar criticality of the SYK baths has direct consequences on the thermal conductance, which above a temperature T∗(V)∼V4T^*(V)\sim V^4T∗(V)∼V4 is parametrically enhanced with respect to the linear-TTT behavior expected in systems with quasiparticles. Interestingly, below T∗(V)T^*(V)T∗(V) the linear thermal conductance behavior is restored, yet transport is not due to quasiparticles. Rather the system gets strongly renormalized by the strange bath and becomes Non-Fermi-Liquid and maximally chaotic. Finally, we discuss the full nonequilibrium energy current and show that its form is compatible with the structure J=Φ(TL)−Φ(TR)\mathcal{J}=Φ(T_L)-Φ(T_R)J=Φ(TL​)−Φ(TR​), with Φ(T)∼TγΦ(T)\sim T^γΦ(T)∼Tγ and power law crossing over from γ=3/2γ=3/2γ=3/2 to γ=2γ=2γ=2 below T∗T^*T∗.