Universität zu Köln

Altland, Alexander ORCID: 0000-0002-2991-4805 and Bagrets, Dmitry ORCID: 0000-0002-3985-4834 (2018). Quantum ergodicity in the SYK model. Nucl. Phys. B, 930. S. 45 - 69. AMSTERDAM: ELSEVIER SCIENCE BV. ISSN 1873-1562

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Abstract

We present a replica path integral approach describing the quantum chaotic dynamics of the SYK model at large time scales. The theory leads to the identification of non-ergodic collective modes which relax and eventually give way to an ergodic long time regime (describable by random matrix theory). These modes, which play a role conceptually similar to the diffusion modes of dirty metals, carry quantum numbers which we identify as the generators of the Clifford algebra: each of the 2(N) different products that can be formed from N Majorana operators defines one effective mode. The competition between a decay rate quickly growing in the order of the product and a density of modes exponentially growing in the same parameter explains the characteristics of the system's approach to the ergodic long time regime. We probe this dynamics through various spectral correlation functions and obtain favorable agreement with existing numerical data. (C) 2018 The Authors. Published by Elsevier B.V.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Altland, Alexander UNSPECIFIED orcid.org/0000-0002-2991-4805 UNSPECIFIED Bagrets, Dmitry UNSPECIFIED orcid.org/0000-0002-3985-4834 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-187431
DOI:	10.1016/j.nuclphysb.2018.02.015
Journal or Publication Title:	Nucl. Phys. B
Volume:	930
Page Range:	S. 45 - 69
Date:	2018
Publisher:	ELSEVIER SCIENCE BV
Place of Publication:	AMSTERDAM
ISSN:	1873-1562
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Physics > Institute for Theoretical Physics
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language DISTRIBUTIONS; STATISTICS; LEVEL Multiple languages Physics, Particles & Fields Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/18743