Universal Statistics of Topological Defects Formed in a Quantum Phase Transition

TL;DR

This paper investigates the universal statistical properties of topological defects formed during quantum phase transitions, revealing that their distribution follows a universal power-law scaling and approaches a normal distribution in large systems.

Contribution

It provides the exact full counting statistics of kinks in the transverse-field quantum Ising model, demonstrating universal scaling behavior of all cumulants with the quench rate.

Findings

Kink number distribution follows a Poisson binomial distribution.

All cumulants exhibit universal power-law scaling with quench rate.

Distribution approaches a normal distribution in the thermodynamic limit.

Abstract

When a quantum phase transition is crossed in finite time, critical slowing down leads to the breakdown of adiabatic dynamics and the formation of topological defects. The average density of defects scales with the quench rate following a universal power-law predicted by the Kibble-Zurek mechanism. We analyze the full counting statistics of kinks and report the exact kink number distribution in the transverse-field quantum Ising model. Kink statistics is described by the Poisson binomial distribution with all cumulants exhibiting a universal power-law scaling with the quench rate. In the absence of finite-size effects, the distribution approaches a normal one, a feature that is expected to apply broadly in systems described by the Kibble-Zurek mechanism.