Emergence of unitary symmetry of microcanonically truncated operators in chaotic quantum systems

verfasst von

Jiaozi Wang, Jonas Richter, Mats H. Lamann, Robin Steinigeweg, Jochen Gemmer, Anatoly Dymarsky

Abstract

We study statistical properties of matrix elements of observables written in the energy eigenbasis and truncated to small microcanonical windows. We present numerical evidence indicating that for all few-body operators in chaotic many-body systems, truncated below a certain energy scale, collective statistical properties of matrix elements exhibit emergent unitary symmetry. Namely, we show that below a certain scale the spectra of the truncated operators exhibit universal behavior, matching our analytic predictions, which are numerically testable for system sizes beyond exact diagonalization. We discuss operator and system-size dependence of the energy scale of emergent unitary symmetry and put our findings in the context of previous works exploring the emergence of random-matrix behavior at small energy scales.

Organisationseinheit(en)

Institut für Theoretische Physik

Externe Organisation(en)

Universität Osnabrück
Stanford University
University of Kentucky

Typ

Letter

Journal

Physical Review E

Band

110

Anzahl der Seiten

6

ISSN

2470-0045

Publikationsdatum

27.09.2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Statistische und nichtlineare Physik, Statistik und Wahrscheinlichkeit, Physik der kondensierten Materie

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2310.20264 (Zugang: Offen)
https://doi.org/10.1103/PhysRevE.110.L032203 (Zugang: Geschlossen)