Long-lived interacting phases of matter protected by multiple time-translation symmetries in quasiperiodically-driven systems

TL;DR

This paper introduces a new class of nonequilibrium phases of matter arising from multiple incommensurate time-translation symmetries in quasiperiodically driven quantum systems, including time quasicrystals and topological phases.

Contribution

It establishes conditions for the stability of these phases and develops a formalism to classify and construct explicit examples of them, advancing understanding of driven many-body systems.

Findings

Identification of stable nonequilibrium phases under quasiperiodic driving.

Construction of explicit models exhibiting time quasi-crystals.

Classification of phases protected by multiple time-translation symmetries.

Abstract

We show how a large family of interacting nonequilibrium phases of matter can arise from the presence of multiple time-translation symmetries, which occur by quasiperiodically driving an isolated quantum many-body system with two or more incommensurate frequencies. These phases are fundamentally different from those realizable in time-independent or periodically-driven (Floquet) settings. Focusing on high-frequency drives with smooth time-dependence, we rigorously establish general conditions for which these phases are stable in a parametrically long-lived `preheating' regime. We develop a formalism to analyze the effect of the multiple time-translation symmetries on the dynamics of the system, which we use to classify and construct explicit examples of the emergent phases. In particular, we discuss time quasi-crystals which spontaneously break the time-translation symmetries, as well as time-translation symmetry protected topological phases.