Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies
Year: 2020
Type: article
Abstract: Using numerical exact diagonalization, we study matrix elements of a local spin operator in the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the question to what extent local operators can be represented as random matrices and, in particular, to what extent matrix elements can be considered as uncorrelated. As a main result, we show that the eigenvalue distribution of band submatrices at a fixed energy density is a sensitive probe of the correlations between matrix elements. We find that, on the scales where the matrix elements are in a good agreement with all standard indicators of the eigenstate thermalization hypothesis, the eigenvalue distribution still exhibits clear signatures of the original operator, implying correlations between matrix elements. Moreover, we demonstrate that at much smaller energy scales, the eigenvalue distribution approximately assumes the universal semicircle shape, indicating transition to the random-matrix behavior, and in particular that matrix elements become uncorrelated.
Source: Physical review. E
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Awards: Nichtgleichgewichtsdynamik in 2D Clustern aus der
Perspektive von Quantentypikalität und Eigenzustandsthermalisierung, FOR 2692: Fundamental Aspects of Statistical Mechanics and the Emergence of Thermodynamics in NonEquilibrium Systems, G3253820483, G4899117297, G5383370051, G62979356, Kombinationen gedämpfter harmonischen Oszillationen als stabile Bausteine von Autokorrelationsfunktionen in Quantenvielteilchensystemen
OpenAlex ID: W3045539009