Constrained dynamics and confinement in the two-dimensional quantum Ising model

TL;DR

This paper studies the constrained dynamics and confinement phenomena in the two-dimensional quantum Ising model, revealing how excitations behave under different regimes and how interfaces evolve after quenches.

Contribution

It provides a detailed analysis of confinement effects, interface dynamics, and the crossover from confining to deconfining regimes in the 2D quantum Ising model.

Findings

Signatures of confinement observed in dynamics

Perturbation theory captures excitation behavior in the confining regime

Identified crossover from resonant to diffusive melting

Abstract

We investigate the dynamics of the quantum Ising model on two-dimensional square lattices up to $16 \times 16$ spins. In the ordered phase, the model is predicted to exhibit dynamically constrained dynamics, leading to confinement of elementary excitations and slow thermalization. After demonstrating the signatures of confinement, we probe the dynamics of interfaces in the constrained regime through sudden quenches of product states with domains of opposite magnetization. We find that the nature of excitations can be captured by perturbation theory throughout the confining regime, and identify the crossover to the deconfining regime. We systematically explore the effect of the transverse field on the modes propagating along flat interfaces and investigate the crossover from resonant to diffusive melting of a square of flipped spins embedded in a larger lattice.