2017/05/31 by Rubem Mondaini, Marcos Rigol · 2 citations
Physics and Astronomy · #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physreve.96.012157
published as Phys. Rev. E 96, 012157 (2017) · 10 pages, 9 figures, as published
arxiv created 2017/08/01 · arxiv updated 2017/08/02
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.