Normal weak eigenstate thermalization

Łydżba, Patrycja (author), Świętek, Rafał (author), Mierzejewski, Marcin (author), Rigol, Marcos (author), Vidmar, Lev (author)

Eigenstate thermalization has been numerically shown to occur for few-body observables in a wide range of nonintegrable models. For intensive sums of few-body observables, a weaker version of eigenstate thermalization known as weak eigenstate thermalization has been proved to occur in general. Here, we unveil a stricter weak eigenstate thermalization phenomenon that occurs in quadratic models exhibiting quantum chaos in the single-particle sector (quantum-chaotic quadratic models) and in integrable interacting models. In such models, we argue that few-body observables that have a properly defined system-size independent norm are guaranteed to exhibit at least a polynomially vanishing variance (over the entire many-body energy spectrum) of the diagonal matrix elements, a phenomenon we dub normal weak eigenstate thermalization. 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 three-dimensional Anderson model in the delocalized regime and the power-law random banded matrix model, as well as for the integrable interacting spin-1/2 XYZ and XXZ models.

• Language: English
• Keywords: quantum chaos, thermalization, localization
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2024
• Number of pages: Str. 104202-1-104202-19
• Numbering: Vol. 110, iss. 10
• PID: 20.500.12556/RUL-165854
• UDC: 538.9
• ISSN on article: 2469-9950
• DOI: 10.1103/PhysRevB.110.104202
• COBISS.SI-ID: 217686275
• Publication date in RUL: 12.12.2024

Record is a part of a journal

• Title: Physical review
• Publisher: American Physical Society
• ISSN: 2469-9950
• COBISS.SI-ID: 2997348

Secondary language

• Language: Slovenian
• Keywords: kvantni kaos, termalizacija, lokalizacija