Loschmidt echoes in two-body random matrix ensembles

TL;DR

This paper investigates fidelity decay in quantum many-body systems with a mean field Hamiltonian plus weak two-body interactions, revealing a slow decay called 'freeze' that explains mean field theories' success.

Contribution

It introduces a linear response solution within a random matrix framework showing the 'freeze' phenomenon in fidelity decay, supported by numerical evidence.

Findings

Median fidelity decay exhibits 'freeze' behavior.

Ground state fidelity also shows 'freeze' on average.

Numerical simulations confirm the slow decay phenomenon.

Abstract

Fidelity decay is studied for quantum many-body systems with a dominant independent particle Hamiltonian resulting e.g. from a mean field theory with a weak two-body interaction. The diagonal terms of the interaction are included in the unperturbed Hamiltonian, while the off-diagonal terms constitute the perturbation that distorts the echo. We give the linear response solution for this problem in a random matrix framework. While the ensemble average shows no surprising behavior, we find that the typical ensemble member as represented by the median displays a very slow fidelity decay known as ``freeze''. Numerical calculations confirm this result and show, that the ground state even on average displays the freeze. This may contribute to explanation of the ``unreasonable'' success of mean field theories.