• Editors' Suggestion

Supersymmetry method for interacting chaotic and disordered systems: The Sachdev-Ye-Kitaev model

Tigran A. Sedrakyan and Konstantin B. Efetov
Phys. Rev. B 102, 075146 – Published 31 August 2020

Abstract

The nonlinear supermatrix σ model is widely used to understand the physics of Anderson localization and the level statistics in noninteracting disordered electron systems. In contrast to the general belief that the supersymmetry method applies only to systems of noninteracting particles, we adopt this approach to the disorder averaging in the interacting models. In particular, we apply supersymmetry to study the Sachdev-Ye-Kitaev (SYK) model where the disorder averaging has so far been performed only within the replica approach. We use a slightly modified time-reversal invariant version of the SYK model and perform calculations in real time. As a demonstration of how the supersymmetry method works, we derive saddle-point equations. In the semiclassical limit, we show that the results are in agreement with those found using the replica technique. We also develop the formally exact superbosonized representation of the SYK model. In the latter, the supersymmetric theory of original fermions and their superpartner bosons is reformulated as a model of unconstrained collective excitations. We argue that the supersymmetry description of the model paves the way for precise calculations in SYK-like models used in condensed matter, gravity, and high-energy physics.

  • Received 27 February 2020
  • Revised 30 June 2020
  • Accepted 10 August 2020

DOI:https://doi.org/10.1103/PhysRevB.102.075146

©2020 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsParticles & Fields

Authors & Affiliations

Tigran A. Sedrakyan1 and Konstantin B. Efetov2,3

  • 1Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
  • 2Ruhr University Bochum, Faculty of Physics and Astronomy, Bochum, 44780, Germany
  • 3National University of Science and Technology “MISiS,” Moscow 119049, Russia

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 102, Iss. 7 — 15 August 2020

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×