Formation and critical dynamics of topological defects in Lifshitz holography

TL;DR

This paper investigates the formation and dynamics of topological defects in a Lifshitz holographic model, confirming Kibble-Zurek scaling laws and extracting critical exponents in a (2+1)-dimensional quantum critical system.

Contribution

It demonstrates the spontaneous generation of magnetic fluxoids and verifies Kibble-Zurek scaling in a Lifshitz holographic setup, revealing critical exponents independent of the Lifshitz exponent.

Findings

Vortex number density scales with quench rate as predicted by Kibble-Zurek.

Critical exponents are consistent across different Lifshitz exponents at finite temperature.

Time lag in condensate evolution indicates nonequilibrium dynamics.

Abstract

We examine the formation and critical dynamics of topological defects via Kibble-Zurek mechanism in a (2+1)-dimensional quantum critical point, which is conjectured to dual to a Lifshitz geometry. Quantized magnetic fluxoids are spontaneously generated and trapped in the cores of order parameter vortices, which is a feature of type II superconductors. Time evolution of the average condensate is found to lag behind the instantaneous equilibrium value of the order parameter, a typical phenomenon in nonequilibrium dynamics. Scalings of vortex number density and the "freeze-out" time match the predictions from Kibble-Zurek mechanism. From these scalings, the dynamic and static critical exponents in the boundary field theory are found, at least at finite temperature, to be irrespective of the Lifshitz exponent in the bulk.