Nonlocal discrete time crystals in periodically driven surface codes

TL;DR

This paper introduces a new type of nonlocal discrete time crystal in a periodically driven surface code, revealing complex phases and topological properties through numerical analysis.

Contribution

It demonstrates the existence of nonlocal DTC phases in a surface code, expanding the understanding of nonequilibrium topological phases in quantum systems.

Findings

Identification of nonlocal period-doubling DTC phase

Discovery of nonlocal period-quadrupling DTC phase

System can also be in trivial or surface code phases

Abstract

Discrete time crystals (DTCs) are nonequilibrium phases of matter characterized by robust subharmonic order parameter dynamics. We report a new type of DTC in a periodically driven surface code, the subharmonic signature of which is only observable with respect to some nonlocal order parameter. By modifying the commonly used metrics for characterizing ordinary DTCs, i.e., the spectral functions, spin-glass order parameters, and two-point correlators, we numerically investigate the different phases of the proposed system. Specifically, depending on the system parameters and boundary conditions, we find that the system may fall into either a "surface code" phase, trivial paramagnet phase, nonlocal period-doubling DTC phase, or nonlocal period-quadrupling DTC phase. Our work thus demonstrates the prospect of exploring topological codes for discovering novel phases of matter.