Criticality and Rigidity of Dissipative Discrete Time Crystals in Solids

TL;DR

This paper investigates dissipative discrete time crystals in a driven quantum Ising model, showing that low-temperature dissipation stabilizes DTC order, reveals new phase transitions, and demonstrates robustness and potential for experimental realization in solids.

Contribution

It introduces a microscopic description of dissipative DTCs in solids, analyzes their phase transitions, and explores the effects of imperfections and reentrant behavior, advancing understanding of nonequilibrium quantum phases.

Findings

Dissipation stabilizes DTC order without fine-tuning at low temperatures.

Reentrant DTC phase transitions occur due to interplay of drive and dissipation.

DTC robustness persists against small pulse imperfections, with possible emergence of DTQCs.

Abstract

We consider a dissipative quantum Ising model periodically driven by a train of $\pi$-pulses and investigate dissipative discrete time crystals (DTCs) in solids. In this model, the interaction between the spins spontaneously breaks the discrete time translation symmetry, giving rise to a dissipative DTC, where two ferromagnetic states are switched alternately by each pulse. We microscopically describe the generic dissipation due to thermal contact to an equilibrium heat bath using the Bloch-Redfield equation. In contrast to other DTC studies, this dissipation stabilizes, rather than destroys, the DTC order without fine-tuning as long as the temperature is low enough. Invoking the time-dependent mean-field theory and solving self-consistently the periodic drive, dissipation, and DTC order parameter, we investigate the nonequilibrium DTC phase transition and determine the critical exponents, including a dynamical one. We also find phase transitions without equilibrium counterpart: a nontrivial interplay of the periodic drive and dissipation gives rise to reentrant DTC transition when changing the pulse interval at a fixed temperature. Besides, to demonstrate the rigidity of the DTC, we consider imperfect $\pi$-pulses, showing that the DTC is robust against the small imperfections and finding that discrete time quasicrystals (DTQC) can appear for the larger imperfections. Together with experimental proposals in magnetic materials, our results pave the ways for realizing the DTC and for uncovering nonequilibrium critical phenomena in real solid-state materials.