Topological Time Crystals

TL;DR

This paper introduces the concept of topological time crystals, where periodically driven systems exhibit topological insulator behavior in the time domain, revealing edge states localized in time.

Contribution

It demonstrates the realization of topological insulators in time within periodically driven systems, including models like SSH in time and driven many-body Bose Haldane insulators.

Findings

Topological edge states can localize in time in driven systems.

Periodically driven systems can host topological phases analogous to spatial topological insulators.

Edge-time states are observable in specific models like SSH and Bose Haldane insulators.

Abstract

By analogy with the formation of space crystals, crystalline structures can also appear in the time domain. While in the case of space crystals we often ask about periodic arrangements of atoms in space at a moment of a detection, in time crystals the role of space and time is exchanged. That is, we fix a space point and ask if the probability density for detection of a system at this point behaves periodically in time. Here, we show that in periodically driven systems it is possible to realize topological insulators, which can be observed in time. The bulk-edge correspondence is related to the edge in time, where edge states localize. We focus on two examples: Su-Schrieffer-Heeger (SSH) model in time and Bose Haldane insulator which emerges in the dynamics of a periodically driven many-body system.