Eigenstate thermalization in the two-dimensional transverse field Ising model: II. Off-diagonal matrix elements of observables
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.
Keywords
Cite
@article{arxiv.1705.08058,
title = {Eigenstate thermalization in the two-dimensional transverse field Ising model: II. Off-diagonal matrix elements of observables},
author = {Rubem Mondaini and Marcos Rigol},
journal= {arXiv preprint arXiv:1705.08058},
year = {2017}
}
Comments
10 pages, 9 figures, as published