Normal weak eigenstate thermalization

• URL: http://arxiv.org/abs/2404.02199v1
• Date: Tue, 2 Apr 2024 18:00:02 GMT
• Title: Normal weak eigenstate thermalization
• Authors: Patrycja Łydżba, Rafał Świętek, Marcin Mierzejewski, Marcos Rigol, Lev Vidmar,
• Abstract summary: Eigenstate thermalization has been shown to occur for few-body observables in a wide range of nonintegrable interacting models. We show that there are few-body observables with a nonvanishing Hilbert-Schmidt norm that are guarrantied to exhibit a vanishing variance of the diagonal matrix elements. For quantum-chaotic quadratic Hamiltonians, we prove that normal weak eigenstate thermalization is a consequence of single-particle eigenstate thermalization.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Eigenstate thermalization has been shown to occur for few-body observables in a wide range of nonintegrable interacting models. For intensive observables that are sums of local operators, because of their polynomially vanishing Hilbert-Schmidt norm, weak eigenstate thermalization occurs in quadratic and integrable interacting systems. Here, we unveil a novel weak eigenstate thermalization phenomenon that occurs in quadratic models whose single-particle sector exhibits quantum chaos (quantum-chaotic quadratic models) and in integrable interacting models. In such models, we show that there are few-body observables with a nonvanishing Hilbert-Schmidt norm that are guarrantied to exhibit a polynomially vanishing variance of the diagonal matrix elements, a phenomenon we dub normal weak eigenstate thermalization. For quantum-chaotic quadratic Hamiltonians, we prove that normal weak eigenstate thermalization is a consequence of single-particle eigenstate thermalization, i.e., it can be viewed as a manifestation of quantum chaos at the single-particle level. We report numerical evidence of normal weak eigenstate thermalization for quantum-chaotic quadratic models such as the 3D Anderson model in the delocalized regime and the power-law random banded matrix model, as well as for the integrable interacting spin-$\frac{1}{2}$ XYZ and XXZ models.

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