Topologically protected boundary discrete time crystal for a solvable model

TL;DR

This paper introduces a solvable spin chain model that demonstrates topologically protected boundary discrete time crystal behavior, linking Floquet topological phases with robust sub-harmonic oscillations in non-equilibrium systems.

Contribution

It presents a new exactly solvable model for Floquet time crystals, connecting topological invariants with DTC robustness and edge states.

Findings

Topologically protected edge states generate sub-harmonic oscillations.

DTC phase is robust against certain symmetry-preserving and breaking perturbations.

The model provides insights into DTC behavior in interacting and dissipative systems.

Abstract

Floquet time crystal, which breaks discrete time-translation symmetry, is an intriguing phenomenon in non-equilibrium systems. It is crucial to understand the rigidity and robustness of discrete time crystal (DTC) phases in a many-body system, and finding a precisely solvable model can pave a way for understanding of the DTC phase. Here, we propose and study a solvable spin chain model by mapping it to a Floquet superconductor through the Jordan-Wigner transformation. The phase diagrams of Floquet topological systems are characterized by topological invariants and tell the existence of anomalous edge states. The sub-harmonic oscillation, which is the typical signal of the DTC, can be generated from such edge states and protected by topology. We also examine the robustness of the DTC by adding symmetry-preserving and symmetry-breaking perturbations. Our results on topologically protected DTC can provide a deep understanding of the DTC when generalized to other interacting or dissipative systems.