Dynamical Ginzburg criterion for the quantum-classical crossover of the Kibble-Zurek mechanism

TL;DR

This paper introduces a dynamical Ginzburg criterion to predict the quantum-classical crossover in the Kibble-Zurek mechanism for lattice models, validated through tensor network simulations of the quantum Ising model.

Contribution

It proposes a simple, quantitative criterion for the crossover, applicable to lattice models, and demonstrates its validity through numerical simulations and finite-time scaling analysis.

Findings

The crossover is a general feature of lattice critical models.

The dynamical Ginzburg criterion accurately predicts the crossover.

Numerical simulations confirm the criterion's validity.

Abstract

We introduce a simple criterion for lattice models to predict quantitatively the crossover between the classical and the quantum scaling of the Kibble-Zurek mechanism, as the one observed in a quantum $\phi^4$-model on a 1D lattice [Phys. Rev. Lett. 116, 225701 (2016)]. We corroborate that the crossover is a general feature of critical models on a lattice, by testing our paradigm on the quantum Ising model in transverse field for arbitrary spin-$s$ ($s \geq 1/2$) in one spatial dimension. By means of tensor network methods, we fully characterize the equilibrium properties of this model, and locate the quantum critical regions via our dynamical Ginzburg criterion. We numerically simulate the Kibble-Zurek quench dynamics and show the validity of our picture, also according to finite-time scaling analysis.