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DY: Fachverband Dynamik und Statistische Physik

DY 17: Many-body Systems: Equilibration, Chaos, and Localization (joint session DY/TT)

DY 17.12: Talk

Tuesday, March 19, 2024, 12:30–12:45, A 151

Weak eigenstate thermalization hypothesis — Patrycja Łydzba¹, •Rafał Świetek^2,3, Marcin Mierzejewski¹, Marcos Rigol⁴, and Lev Vidmar^2,3 — ¹Institute of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, 50-370 Wrocław, Poland — ²Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia — ³Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia — ⁴Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA

While the eigenstate thermalization hypothesis (ETH) is well established for quantum-chaotic interacting systems, its validity for other classes of systems remains a matter of intense debate. Focusing on quadratic fermionic Hamiltonians, we here argue that the weak ETH is satisfied for few-body observables in many-body eigenstates of quantum-chaotic quadratic (QCQ) Hamiltonians. In contrast, the weak ETH is violated for few-body observables in localized quadratic Hamiltonians. We argue that these properties can be traced back to the validity of single-particle eigenstate thermalization, and we highlight the subtle role of normalization of operators. Our results suggest that the difference between weak and no ETH in many-body eigenstates allows for a distinction between single-particle quantum chaos and localization. We test to which degree this phenomenology holds true for integrable systems such as the XYZ and XXZ models.

Keywords: single particle chaos; equilibration; eigenstate thermalization hypothesis