Stabilizing boundary time crystals through Non-markovian dynamics

TL;DR

This paper demonstrates that non-Markovian dynamics can effectively stabilize boundary time crystals and induce higher-order limit cycles, expanding understanding of dissipative time-translation symmetry breaking.

Contribution

It reveals the beneficial role of non-Markovian effects in stabilizing boundary time crystals and introduces the emergence of higher-order limit cycles in such systems.

Findings

Non-Markovian dynamics stabilize BTCs over a wide parameter range.

Higher-order limit cycles emerge under certain non-Markovian conditions.

Complex behaviors are observed with varying non-Markovianity parameters.

Abstract

We study Boundary time crystals (BTCs) in the presence of non-Markovian dynamics. In contrast to BTCs observed in earlier works in the Markovian regime, we show that non-Markovian dynamics can be highly beneficial for stabilizing BTCs over a wide range of parameter values, even in the presence of intermediate rates of dissipation. Notably, we also observe the emergence of higher-order limit cycles (HO-LCs) for some parameter regimes. We analyze the effect of non-Markovian dynamics on BTCs and HO-LCs using quantum Fisher information, time-averaged magnetization, a measure of non-Markovianity, and a dynamical phase diagram, all of which show complex behaviors with changing non-Markovianity parameters. Our studies can pave the way for stabilizing time crystals in dissipative systems, as well as lead to studies on varied dissipative dynamics on time translational symmetry breaking.