From operator statistics to wormholes - Kölner UniversitätsPublikationsServer

Altland, Alexander, Bagrets, Dmitry ORCID: 0000-0002-3985-4834, Nayak, Pranjal, Sonner, Julian and Vielma, Manuel (2021). From operator statistics to wormholes. Phys. Rev. Res., 3 (3). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2643-1564

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DOI:10.1103/PhysRevResearch.3.033259

Abstract

For a generic quantum many-body system, the quantum ergodic regime is defined as the limit in which the spectrum of the system resembles that of a random matrix theory (RMT) in the corresponding symmetry class. In this paper, we analyze the time dependence of correlation functions of operators. We study them in the ergodic limit as well as their approach to the ergodic limit, which is controlled by nonuniversal massive modes. An effective field theory (EFT) corresponding to the causal symmetry and its breaking describes the ergodic phase. We demonstrate that the resulting Goldstone-mode theory has a topological expansion, analogous to the one described by Altland and Sonner [SciPost Phys. 11, 034 (2021)] with added operator sources, whose leading nontrivial topologies give rise to the universal ramp seen in correlation functions. The ergodic behavior of operators in our EFT is seen to result from a combination of RMT-like spectral statistics and Haar averaging over wave functions. Furthermore, we capture analytically the plateau behavior by taking into account the contribution of a second saddle point. Our main interest is quantum many-body systems with holographic duals, and we explicitly establish the validity of the EFT description in the Sachdev-Ye-Kitaev class of models, starting from their microscopic description. By studying the tower of massive modes above the Goldstone sector, we get a detailed understanding of how the ergodic EFT phase is approached, and we derive the relevant Thouless timescales. We point out that the topological expansion can be reinterpreted in terms of contributions of bulk wormholes and baby universes.

Item Type:

Journal Article

Creators:

Creators	Email	ORCID	ORCID Put Code
Altland, Alexander	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Bagrets, Dmitry	UNSPECIFIED	orcid.org/0000-0002-3985-4834	UNSPECIFIED
Nayak, Pranjal	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Sonner, Julian	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Vielma, Manuel	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED