Floquet time crystals in driven spin systems with all-to-all $p$-body interactions

TL;DR

This paper demonstrates the existence of Floquet time crystal phases in driven all-to-all p-spin models, revealing new period-multiplied responses and analyzing their stability and connection to quantum phase transitions.

Contribution

It introduces a comprehensive framework for predicting and characterizing robust subharmonic responses in p-spin models, including novel period-quadrupling phases for p=4.

Findings

Existence of period-doubling and quadrupling time crystals in p-spin models

Development of a classical map framework to predict time crystal stability

Connection between time crystal emergence and quantum phase transitions

Abstract

We show the emergence of Floquet time crystal (FTC) phases in the Floquet dynamics of periodically driven $p$-spin models, which describe a collection of spin-1/2 particles with all-to-all $p$-body interactions. Given the mean-field nature of these models, we treat the problem exactly in the thermodynamic limit and show that, for a given $p$, these systems can host various robust time-crystalline responses with period $nT$, where $T$ is the period of the drive and $n$ an integer between 2 and $p$. In particular, the case of four-body interactions ($p=4$) gives rise to both a usual period-doubling crystal, and also a novel period-quadrupling phase. We develop a comprehensive framework to predict robust subharmonic response in classical area-preserving maps, and use this as a basis to predict the occurrence and characterize the stability of the resulting mean-field FTC phases in the quantum regime. Our analysis reveals that the robustness of the time-crystal behavior is reduced as their period increases, and establishes a connection between the emergence of time crystals, described by eigenstate ordering and robust subharmonic response, and the phenomenology of excited state and dynamical quantum phase transitions. Finally, for the models hosting two or more coexisting time crystal phases, we define protocols where the periodic subharmonic response of the system can be varied in time via the non-periodic modulation of an external control parameter.