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

Understand

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.