Criticality and rigidity of dissipative discrete time crystals in solids

We consider a dissipative quantum Ising model periodically driven by a train of n 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 an 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. Also, 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 can appear for the larger imperfections. Together with experimental proposals in magnetic materials, our results pave the way for realizing the DTC and for uncovering nonequilibrium critical phenomena in real solid-state materials.

Automated summary

We investigate dissipative discrete time crystals (DTCs) in solids, where a dissipative quantum Ising model is periodically driven by a train of pulses. The interaction between the spins breaks the discrete time translation symmetry and results in a dissipative DTC, where two ferromagnetic states switch alternately by each pulse. Unlike other DTC studies, we find that the dissipation in this model stabilizes the DTC order without fine-tuning at low temperatures. We study the nonequilibrium DTC phase transition and determine the critical exponents using a time-dependent mean-field theory. We also observe phase transitions without an equilibrium counterpart due to the interplay of the periodic drive and dissipation. Additionally, we demonstrate the robustness of the DTC against small imperfections and find that discrete time quasicrystals can appear for larger imperfections. Our results pave the way for realizing the DTC and uncovering nonequilibrium critical phenomena in real solid-state materials.