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Eigenstate thermalization in the two-dimensional transverse field Ising model. II. Off-diagonal matrix elements of observables

2017; American Physical Society; Volume: 96; Issue: 1 Linguagem: Inglês

10.1103/physreve.96.012157

2470-0061

Rubem Mondaini, Marcos Rigol,

Opinion Dynamics and Social Influence

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.