Probing Confinement Through Dynamical Quantum Phase Transitions: From Quantum Spin Models to Lattice Gauge Theories

TL;DR

This paper demonstrates that dynamical quantum phase transitions serve as indicators of confinement and deconfinement in quantum many-body systems, revealing qualitative changes in non-equilibrium critical behavior across different models.

Contribution

It introduces a large-scale matrix product state approach to identify distinct dynamical quantum phase transitions associated with confinement phenomena in various quantum models.

Findings

Branch and manifold DQPTs are signatures of (de)confinement.

Manifold DQPTs relate to order parameter sign change.

Branch DQPTs occur despite constrained order parameter dynamics.

Abstract

Confinement is an intriguing phenomenon prevalent in condensed matter and high-energy physics. Exploring its effect on the far-from-equilibrium criticality of quantum many-body systems is of great interest both from a fundamental and technological point of view. Here, we employ large-scale uniform matrix product state calculations to show that a qualitative change in the type of dynamical quantum phase transitions (DQPTs) accompanies the confinement-deconfinement transition in three paradigmatic models -- the power-law interacting quantum Ising chain, the two-dimensional quantum Ising model, and the spin-$S$ $\mathrm{U}(1)$ quantum link model. By tuning a confining parameter in these models, it is found that \textit{branch} (\textit{manifold}) DQPTs arise as a signature of (de)confinement. Whereas manifold DQPTs are associated with a sign change of the order parameter, their branch counterparts are not, but rather occur even when the order parameter exhibits considerably constrained dynamics. Our conclusions can be tested in modern quantum-simulation platforms, such as ion-trap setups and cold-atom experiments of gauge theories.