Localization and melting of interfaces in the two-dimensional quantum Ising model

TL;DR

This paper investigates the non-equilibrium dynamics of ferromagnetic interfaces in the 2D quantum Ising model, revealing integrable interface excitations, effects of symmetry-breaking fields, and conditions for bubble melting.

Contribution

It introduces a holographic mapping to study interface excitations as an integrable fermionic chain and explores ergodicity breaking due to Stark many-body localization.

Findings

Interface excitations map to an integrable fermionic chain.

Symmetry-breaking fields induce ergodicity breaking and localization.

A lower bound on bubble melting timescales is provided.

Abstract

We study the non-equilibrium evolution of coexisting ferromagnetic domains in the two-dimensional quantum Ising model -- a setup relevant in several contexts, from quantum nucleation dynamics and false-vacuum decay scenarios to recent experiments with Rydberg-atom arrays. We demonstrate that the quantum-fluctuating interface delimiting a large bubble can be studied as an effective one-dimensional system through a "holographic" mapping. For the considered model, the emergent interface excitations map to an integrable chain of fermionic particles. We discuss how this integrability is broken by geometric features of the bubbles and by corrections in inverse powers of the ferromagnetic coupling, and provide a lower bound to the timescale after which the bubble is ultimately expected to melt. Remarkably, we demonstrate that a symmetry-breaking longitudinal field gives rise to a robust ergodicity breaking in two dimensions, a phenomenon underpinned by Stark many-body localization of the emergent fermionic excitations of the interface.