Non-Gaussian distribution of collective operators in quantum spin chains

TL;DR

This paper investigates the full distribution of collective observables in quantum spin chains, revealing non-Gaussian behavior at criticality and demonstrating the potential for experimental measurement using light-matter interfaces.

Contribution

It shows how quantum fluctuations cause non-Gaussian distributions at critical points and demonstrates the collapse of scaled distributions across different system sizes.

Findings

Distributions become highly non-Gaussian at criticality.

Scaled distributions collapse across system sizes.

Feasibility of experimental reconstruction using optical setups.

Abstract

We numerically analyse the behavior of the full distribution of collective observables in quantum spin chains. While most of previous studies of quantum critical phenomena are limited to the first moments, here we demonstrate how quantum fluctuations at criticality lead to highly non-Gaussian distributions thus violating the central limit theorem. Interestingly, we show that the distributions for different system sizes collapse after scaling on the same curve for a wide range of transitions: first and second order quantum transitions and transitions of the Berezinskii-Kosterlitz-Thouless type. We propose and carefully analyse the feasibility of an experimental reconstruction of the distribution using light-matter interfaces for atoms in optical lattices or in optical resonators.