# Localization and symmetry breaking in the quantum quasiperiodic Ising glass

## TL;DR

This paper explores how quasiperiodic modulation in quantum Ising chains leads to a stable, long-range ordered glass phase at all energy densities, revealing novel localization and symmetry-breaking phenomena.

## Contribution

It introduces the concept of a quasiperiodic Ising glass and analyzes its stability, phase diagram, and transition properties, extending Aubry-André duality to this context.

## Key findings

- Existence of a stable quasiperiodic Ising glass phase.
- Rich zero-temperature phase diagram with multiple ground states.
- Unusual quantum Ising transition with intermediate properties.

## Abstract

Quasiperiodic modulation can prevent isolated quantum systems from equilibrating by localizing their degrees of freedom. In this article, we show that such systems can exhibit dynamically stable long-range orders forbidden in equilibrium. Specifically, we show that the interplay of symmetry breaking and localization in the quasiperiodic quantum Ising chain produces a \emph{quasiperiodic Ising glass} stable at all energy densities. The glass order parameter vanishes with an essential singularity at the melting transition with no signatures in the equilibrium properties. The zero temperature phase diagram is also surprisingly rich, consisting of paramagnetic, ferromagnetic and quasiperiodically alternating ground state phases with extended, localized and critically delocalized low energy excitations. The system exhibits an unusual quantum Ising transition whose properties are intermediate between those of the clean and infinite randomness Ising transitions. Many of these results follow from a geometric generalization of the Aubry-Andr\'e duality which we develop. The quasiperiodic Ising glass may be realized in near term quantum optical experiments.