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A note on weak eigenstate thermalization and normalization of operators

December 13, 2023 @ 20:15 - 20:30 CET

P. Łydżba,1 R. Świętek,2,3 M. Mierzejewski,1 M. Rigol,4 L. Vidmar2,3

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 in two cases: (a) for sums of few-body observables in all quadratic Hamiltonians, and (b) 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.


December 13, 2023
20:15 - 20:30 CET
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