Non-Hermitian Discrete Time Crystals

TL;DR

This paper introduces a novel approach to stabilize discrete time crystals in open quantum systems using non-Hermitian Hamiltonians with non-reciprocal couplings, preventing thermalization and enhancing robustness against imperfections.

Contribution

It proposes a new mechanism employing non-Hermitian dynamics to realize stable DTCs, addressing decoherence and thermalization issues in driven many-body systems.

Findings

Non-reciprocal couplings prevent thermalization.

Enhanced stability of DTC against pulse imperfections.

Phase diagram characterizing system behavior.

Abstract

Discrete time crystals (DTC) exhibit a special non-equilibrium phase of matter in periodically driven many-body systems with spontaneous breaking of time translational symmetry. The presence of decoherence generally enhances thermalization and destroys the coherence required for the existence of DTC. In this letter, we devise a mechanism for establishing a stable DTC with period-doubling oscillations in an open quantum system that is governed by a properly tailored non-Hermitian Hamiltonian. We find a specific class of non-reciprocal couplings in our non-Hermitian dynamics which prevents thermalization through eigenstate ordering. Such choice of non-Hermitian dynamics, significantly enhances the stability of the DTC against imperfect pulses. Through a comprehensive analysis, we determine the phase diagram of the system in terms of pulse imperfection.