Non-thermal statistics in isolated quantum spin clusters after a series of perturbations

TL;DR

This paper demonstrates that isolated quantum spin clusters exhibit non-thermal energy distributions after perturbations, aligning with quantum micro-canonical ensemble predictions, and suggests eigenstate localization as a protective mechanism for thermalization.

Contribution

It numerically shows non-thermal statistics in quantum spin clusters after perturbations, connecting to the QMC ensemble and highlighting eigenstate localization effects.

Findings

Energy occupations deviate from thermal predictions after perturbations.

Statistics align with the quantum micro-canonical ensemble.

Eigenstates of perturbation operators are localized in energy basis.

Abstract

We show numerically that a finite isolated cluster of interacting spins 1/2 exhibits a surprising non-thermal statistics when subjected to a series of small non-adiabatic perturbations by external magnetic field. The resulting occupations of energy eigenstates are significantly higher than the thermal ones on both the low and the high ends of the energy spectra. This behavior semi-quantitatively agrees with the statistics predicted for the so-called "quantum micro-canonical" (QMC) ensemble, which includes all possible quantum superpositions with a given energy expectation value. Our findings also indicate that the eigenstates of the perturbation operators are generically localized in the energy basis of the unperturbed Hamiltonian. This kind of localization possibly protects the thermal behavior in the macroscopic limit.