Topological Classification of Gapped/Gap-preserving Rational Space-Time Crystal Systems

TL;DR

This paper develops a topological classification framework for rational space-time crystal systems, linking them to Floquet systems and providing analytical solutions and effective Hamiltonians.

Contribution

It introduces a systematic method to classify gapped and gap-preserving rational space-time crystals by relating them to Floquet systems and deriving effective Hamiltonians.

Findings

Rational space-time crystals are equivalent to Floquet systems.

An analytical solution to the Floquet equation is constructed.

A topological classification scheme for these systems is established.

Abstract

The traditional systems researched in condensed matter physics always have spatial translation symmetry. However for space-time crystal systems, the spatial translation symmetry is no longer preserved and the lattice potential have space-time translation symmetry instead. We show that a rational space-time crystal system is equal to a traditional floquet system. Then, we find a way to solve the floquet equation analytically and construct an effective Hamiltonian of the rational space-time crystal system. By this effective Hamiltonian, we obtain the topological classification of gapped and gap-preserving rational space-time crystal systems. Our works reveal the correlation between space-time crystal systems and floquet systems and give a systematic method to explore the properties of rational space-time crystal systems.