Unveiling Eigenstate Thermalization for Non-Hermitian systems

Year: 2025

Authors: Roy S.S., Bandyopadhyay S., de Almeida R.C., Hauke P.

Autors Affiliation: Univ Trento, Pitaevskii BEC Ctr, CNR INO, Via Sommarive 14, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, Via Sommarive 14, I-38123 Trento, Italy; Indian Inst Technol ISM Dhanbad, Dept Phys, IN-826004 Dhanbad, India.

Abstract: The eigenstate thermalization hypothesis (ETH) has been highly influential in explaining thermodynamic behavior of closed quantum systems. As of yet, it is unclear whether and how the ETH applies to non-Hermitian systems. Here, we introduce a framework that extends the ETH to non-Hermitian systems, within which expectation values of local operators reproduce statistical and scaling predictions known from Hermitian ETH. We illustrate the validity of the framework on non-Hermitian random-matrix and Sachdev-Ye-Kitaev models. Further, we show numerically how the static ETH predictions become imprinted onto the dynamics of local observables. Finally, we present a prescription for observing both ETH-obeying and ETH-violating regimes in an optical-lattice experiment that implements a disordered interacting Hatano-Nelson model. Our results generalize the celebrated ETH to the non-Hermitian setting, and they show how it affects the system dynamics, and how the salient signatures can be observed in present-day cold-atom experiments.

Journal/Review: PHYSICAL REVIEW LETTERS

Volume: 134 (18)      Pages from: 180405-1  to: 180405-7

More Information: We gratefully acknowledge useful discussions with Philipp Uhrich. We acknowledge support by the ERC Starting Grant StrEnQTh (Project ID 804305), Provincia Autonoma di Trento, Q@TN; the joint lab between University of Trento, FBK-Fondazione Bruno Kessler, INFN-National Institute for Nuclear Physics, and CNR-National Research Council; and support from ICSC\u2013Centro Nazionale di Ricerca in HPC, Big Data and Quantum Computing, funded by the European Union under NextGenerationEU. The project is funded within the QuantERA II Programme that has received funding from the European Union\u2019s Horizon 2020 research and innovation program under Grant Agreement No. 101017733. This project has received funding from the Italian Ministry of University and Research (MUR) through the FARE grant for the project DAVNE (Grant No. R20PEX7Y3A) and the European Union under Horizon Europe Programme Grant Agreement No. 101080086, NeQST. Funded by the European Union Next Generation EU, Mission 4 Component 2 CUP E53D23002240006. S.\u2009B. acknowledges CINECA for the use of HPC resources under Italian SuperComputing Resource Allocation \u2013 ISCRA Class C Projects No. ISSYK-2 (HP10CP8XXF) and No. DISYK (HP10CGNZG9). S.\u2009S.\u2009R. acknowledges the faculty research scheme at IIT (ISM) Dhanbad, India, under Project No. FRS/2024/PHYSICS/MISC0110.
KeyWords: Many-body Localization; Resonance Fluorescence; Anderson Localization; Quantum; Dynamics; Entanglement; Transitions; Simulation; Breaking; Fermions
DOI: 10.1103/PhysRevLett.134.180405