Kibble-Zurek mechanism in quantum link model

TL;DR

This paper investigates the Kibble-Zurek mechanism in a one-dimensional U(1) lattice gauge theory, revealing the emergence of combined topological defects and their scaling behavior during a quench.

Contribution

It demonstrates the applicability of the Kibble-Zurek mechanism to quantum link models and analyzes the scaling of topological defects and entanglement entropy.

Findings

Combined topological defects include gauge and matter field excitations.

The defect ratio is constrained to 1/2 by Gauss's law.

Electric flux and entanglement entropy follow finite-time scaling laws.

Abstract

We study the driven critical dynamics of the quantum link model, whose Hamiltonian describes the one-dimensional $U(1)$ lattice gauge theory. We find that combined topological defects emerge after the quench and they consist of both gauge field and matter field excitations. Furthermore, the ratio of gauge field and matter field excitation is $1/2$ due to the constraint of the Gauss' law. We show that the scaling of these combined topological defects satisfies the usual Kibble-Zurek mechanism. We verify that both the electric flux and the entanglement entropy satisfy the finite-time scaling theory in the whole driven process. Possible experimental realizations are discussed.