Nonthermal states arising from confinement in one and two dimensions

TL;DR

This paper demonstrates that confinement in quantum Ising models creates nonthermal eigenstates, characterized by meson modes that persist into the spectrum and lead to atypical, nonthermal dynamics in both one and two dimensions.

Contribution

It reveals the existence of nonthermal meson states due to confinement in 1D and 2D quantum Ising models, with analytical and numerical evidence showing their impact on dynamics.

Findings

Meson modes replace the two-particle continuum in the ordered phase.

Nonthermal states cause suppression of entanglement growth and prevent thermalization.

These states are absent in the disordered phase, which thermalizes normally.

Abstract

We show that confinement in the quantum Ising model leads to nonthermal eigenstates, in both continuum and lattice theories, in both one (1D) and two dimensions (2D). In the ordered phase, the presence of a confining longitudinal field leads to a profound restructuring of the excitation spectrum, with the low-energy two-particle continuum being replaced by discrete 'meson' modes (linearly confined pairs of domain walls). These modes exist far into the spectrum and are atypical, in the sense that expectation values in the state with energy $E$ do not agree with the microcanonical (thermal) ensemble prediction. Single meson states persist above the two meson threshold, due to a surprising lack of hybridization with the ($n\geq4$)-domain wall continuum, a result that survives into the thermodynamic limit and that can be understood from analytical calculations. The presence of such states is revealed in anomalous post-quench dynamics, such as the lack of a light cone, the suppression of the growth of entanglement entropy, and the absence of thermalization for some initial states. The nonthermal states are confined to the ordered phase - the disordered (paramagnetic) phase exhibits typical thermalization patterns in both 1D and 2D in the absence of integrability.