Mondaini R, Rigol M. Eigenstate thermalization in the two-dimensional transverse field Ising model. II. Off-diagonal matrix elements of observables.
Phys Rev E 2017;
96:012157. [PMID:
29347111 DOI:
10.1103/physreve.96.012157]
[Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2017] [Indexed: 06/07/2023]
Abstract
We study the matrix elements of few-body observables, focusing on the off-diagonal ones, in the eigenstates of the two-dimensional transverse field Ising model. By resolving all symmetries, we relate the onset of quantum chaos to the structure of the matrix elements. In particular, we show that a general result of the theory of random matrices, namely, the value 2 of the ratio of variances (diagonal to off-diagonal) of the matrix elements of Hermitian operators, occurs in the quantum chaotic regime. Furthermore, we explore the behavior of the off-diagonal matrix elements of observables as a function of the eigenstate energy differences and show that it is in accordance with the eigenstate thermalization hypothesis ansatz.
Collapse