Fidelity decay of the two-level bosonic embedded ensembles of Random Matrices

TL;DR

This paper investigates how fidelity decays in two-level bosonic embedded ensembles of random matrices, revealing revival phenomena, fidelity freeze, and fractional periodic revivals linked to specific k-body interactions.

Contribution

It provides a detailed analysis of fidelity decay, revival, and freeze phenomena in bosonic embedded ensembles, highlighting the role of k-body interactions and scaling properties.

Findings

Fidelity exhibits revival at the Heisenberg time and a fidelity freeze.

Periodic revivals of fidelity occur during the freeze, with periods related to the Heisenberg time.

Fractional revivals are observed, linked to dominant k-body terms in the perturbation.

Abstract

We study the fidelity decay of the $k$-body embedded ensembles of random matrices for bosons distributed over two single-particle states. Fidelity is defined in terms of a reference Hamiltonian, which is a purely diagonal matrix consisting of a fixed one-body term and includes the diagonal of the perturbing $k$-body embedded ensemble matrix, and the perturbed Hamiltonian which includes the residual off-diagonal elements of the $k$-body interaction. This choice mimics the typical mean-field basis used in many calculations. We study separately the cases $k=2$ and $3$. We compute the ensemble-averaged fidelity decay as well as the fidelity of typical members with respect to an initial random state. Average fidelity displays a revival at the Heisenberg time, $t=t_H=1$, and a freeze in the fidelity decay, during which periodic revivals of period $t_H$ are observed. We obtain the relevant scaling properties with respect to the number of bosons and the strength of the perturbation. For certain members of the ensemble, we find that the period of the revivals during the freeze of fidelity occurs at fractional times of $t_H$. These fractional periodic revivals are related to the dominance of specific $k$-body terms in the perturbation.