Light cone dynamics and reverse Kibble-Zurek mechanism in two-dimensional superfluids following a quantum quench

TL;DR

This paper investigates the non-equilibrium dynamics of two-dimensional superfluids after a quantum quench, revealing light cone propagation, a reverse Kibble-Zurek mechanism, and a non-equilibrium phase transition analyzed through numerical and analytical methods.

Contribution

It introduces a combined numerical and analytical study of light cone dynamics and reverse Kibble-Zurek effects in 2D superfluids post-quench, including a new time-dependent RG approach.

Findings

Light cone dynamics observed in superfluid phase evolution.

Identification of a reverse Kibble-Zurek mechanism with vortex unbinding.

Existence of two fixed points corresponding to superfluid and normal states.

Abstract

We study the dynamics of the relative phase of a bilayer of two-dimensional superfluids after the two superfluids have been decoupled. We find that on short time scales the relative phase shows "light cone" like dynamics and creates a metastable superfluid state, which can be supercritical. We also demonstrate similar light cone dynamics for the transverse field Ising model. On longer time scales the supercritical state relaxes to a disordered state due to dynamical vortex unbinding. This scenario of dynamically suppressed vortex proliferation constitutes a reverse-Kibble-Zurek effect. We study this effect both numerically using truncated Wigner approximation and analytically within a newly suggested time dependent renormalization group approach (RG). In particular, within RG we show that there are two possible fixed points for the real time evolution corresponding to the superfluid and normal steady states. So depending on the initial conditions and the microscopic parameters of the Hamiltonian the system undergoes a non-equilibrium phase transition of the Kosterlitz-Thouless type. The time scales for the vortex unbinding near the critical point are exponentially divergent, similar to the equilibrium case.