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.
Highlights
60 years ago, Anderson discovered that quenched disorder could localize quantum particles and prevent the transport necessary for equilibration in isolated systems [1]
A intriguing proposal is that localization can dynamically protect long-range order in highly excited states even when such orders are forbidden in equilibrium [47]
We study the effects of quasiperiodic modulation on the canonical quantum Ising chain
Summary
60 years ago, Anderson discovered that quenched disorder could localize quantum particles and prevent the transport necessary for equilibration in isolated systems [1]. We find that weak quasiperiodic modulation is irrelevant at the clean Ising transition, so the parabolic phase boundary in Fig. 1 exhibits quantum critical scaling with dynamic exponent z 1⁄4 1 and extended low-energy excitations. The noninteracting quasiperiodic models of Azbel, Aubry-André, and their generalizations have been extensively studied by mathematicians and physicists over the last 30 years for a variety of reasons [70,71,72,73,74,75,76,77,78,79,80,81,82] These 1D models exhibit a single-particle localization-delocalization transition at finite modulation which mimics the metal-insulator transition in 3D disordered systems. We conclude with a discussion of the role of interactions, possible experimental realizations, and other open questions
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