Space-time renormalization in phase transition dynamics

TL;DR

This paper investigates a space-time renormalization scaling in quantum critical dynamics, providing evidence through an exact solution of the transverse field quantum Ising chain, inspired by the Kibble-Zurek mechanism.

Contribution

It introduces a novel space-time renormalization framework for quantum phase transition dynamics, supported by an exact analytical solution.

Findings

Demonstrates Kibble-Zurek scaling in quantum Ising chain

Establishes a space-time renormalization analogy with equilibrium critical phenomena

Provides exact evidence for dynamical scaling laws

Abstract

When a system is driven across a quantum critical point at a constant rate its evolution must become non-adiabatic as the relaxation time $\tau$ diverges at the critical point. According to the Kibble-Zurek mechanism (KZM), the emerging post-transition excited state is characterized by a finite correlation length $\hat\xi$ set at the time $\hat t=\hat \tau$ when the critical slowing down makes it impossible for the system to relax to the equilibrium defined by changing parameters. This observation naturally suggests a dynamical scaling similar to renormalization familiar from the equilibrium critical phenomena. We provide evidence for such KZM-inspired spatiotemporal scaling by investigating an exact solution of the transverse field quantum Ising chain in the thermodynamic limit.