Discrete Time Quasi-Crystals

TL;DR

This paper explores how periodically driven quantum many-body systems can spontaneously form quasi-crystal structures in time due to particle interactions, revealing a new phase of matter.

Contribution

It demonstrates the emergence of time quasi-crystals in quantum systems under periodic driving, highlighting a novel form of spontaneous symmetry breaking.

Findings

Spontaneous formation of quasi-crystals in time in driven quantum systems

Interactions induce self-organization into aperiodic temporal structures

Identification of conditions for time quasi-crystal stability

Abstract

Between space crystals and amorphous materials there exists a third class of aperiodic structures which lack translational symmetry but reveal long-range order. They are dubbed quasi-crystals and their formation, similarly as the formation of space crystals, is related to spontaneous breaking of translational symmetry of underlying Hamiltonians. Here, we investigate spontaneous emergence of quasi-crystals in periodically driven systems. We consider a quantum many-body system which is driven by a harmonically oscillating force and show that interactions between particles result in spontaneous self-reorganization of the motion of a quantum many-body system and in the formation of a quasi-crystal structure in time.