Effects of non-integrability in a non-Hermitian time crystal

TL;DR

This paper explores how adding non-integrable interactions affects non-Hermitian time crystals, revealing phase shifts and a new symmetry-breaking transition driven by many-body effects.

Contribution

It introduces the impact of non-integrable interactions on non-Hermitian time crystals, uncovering a novel symmetry-breaking transition not predicted by mean-field theory.

Findings

Interaction shifts phase boundaries

Strong interactions induce symmetry breaking

Transition linked to ferromagnetic phase in XXZ model

Abstract

Time crystals are systems that spontaneously break time-translation symmetry, exhibiting repeating patterns in time. Recent work has shown that non-Hermitian Floquet systems can host a time crystalline phase with quasi-long-range order. In this work, we investigate the effect of introducing a non-integrable interaction term into this non-Hermitian time crystal model. Using a combination of numerical TEBD simulations, mean-field analysis, and perturbation theory, we find that the interaction term has two notable effects. First, it induces a shift in the phase diagram, moving the boundaries between different phases. Second, a sufficiently strong interaction induces an unexpected symmetry-breaking transition, which is not captured by the mean-field approach. Within average Hamiltonian theory, we trace this back to a ferromagnetic transition in the anisotropic non-Hermitian XXZ model. Our results demonstrate that the interplay between non-Hermitian dynamics and many-body interactions can lead to novel symmetry breaking.