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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, and Subir Sachdev
Phys. Rev. B 95, 155131 – Published 18 April 2017
An article within the collection: Physical Review B 50th Anniversary Milestones

Abstract

We compute the thermodynamic properties of the Sachdev-Ye-Kitaev (SYK) models of fermions with a conserved fermion number Q. We extend a previously proposed Schwarzian effective action to include a phase field, and this describes the low-temperature energy and Q fluctuations. We obtain higher-dimensional generalizations of the SYK models which display disordered metallic states without quasiparticle excitations, and we deduce their thermoelectric transport coefficients. We also examine the corresponding properties of Einstein-Maxwell-axion theories on black brane geometries which interpolate from either AdS4 or AdS5 to an AdS2×R2 or AdS2×R3 near-horizon geometry. These provide holographic descriptions of nonquasiparticle metallic states without momentum conservation. We find a precise match between low-temperature transport and thermodynamics of the SYK and holographic models. In both models, the Seebeck transport coefficient is exactly equal to the Q derivative of the entropy. For the SYK models, quantum chaos, as characterized by the butterfly velocity and the Lyapunov rate, universally determines the thermal diffusivity, but not the charge diffusivity.

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  • Received 14 December 2016
  • Revised 17 February 2017

DOI:https://doi.org/10.1103/PhysRevB.95.155131

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsParticles & Fields

Collections

This article appears in the following collection:

Physical Review B 50th Anniversary Milestones

These Milestone studies represent lasting contributions to physics by way of reporting significant discoveries, initiating new areas of research, or substantially enhancing the conceptual tools for making progress in the burgeoning field of condensed matter physics.

Authors & Affiliations

Richard A. Davison1, Wenbo Fu1, Antoine Georges2,3,4, Yingfei Gu5, Kristan Jensen6, and Subir Sachdev1,7

  • 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
  • 2Centre de Physique Théorique, École Polytechnique, CNRS, 91128 Palaiseau Cedex, France
  • 3Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France
  • 4Department of Quantum Matter Physics, University of Geneva, 24 Quai Ernest-Ansermet, 1211 Geneva 4, Switzerland
  • 5Department of Physics, Stanford University, Stanford, California 94305, USA
  • 6Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
  • 7Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5

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Issue

Vol. 95, Iss. 15 — 15 April 2017

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