Universal equilibrium distribution after a small quantum quench

TL;DR

This paper investigates the long-time statistical behavior of quantum observables after small quenches, revealing universal distribution patterns that depend on whether the quench occurs near critical or regular points.

Contribution

It introduces a universal description of equilibrium distributions after small quantum quenches, highlighting a transition from Gaussian to double-peaked distributions near critical points.

Findings

Gaussian distributions for regular points indicating good equilibration

Universal double-peaked distributions near critical points

Numerical validation in a non-integrable quantum Ising model

Abstract

A sudden change of the Hamiltonian parameter drives a quantum system out of equilibrium. For a finite-size system, expectations of observables start fluctuating in time without converging to a precise limit. A new equilibrium state emerges only in probabilistic sense, when the probability distribution for the observables expectations over long times concentrate around their mean value. In this paper we study the full statistic of generic observables after a small quench. When the quench is performed around a regular (i.e. non-critical) point of the phase diagram, generic observables are expected to be characterized by Gaussian distribution functions (``good equilibration''). Instead, when quenching around a critical point a new universal double-peaked distribution function emerges for relevant perturbations. Our analytic predictions are numerically checked for a non-integrable extension of the quantum Ising model.