Nonperturbative decay of bipartite discrete time crystals

TL;DR

This paper demonstrates the existence of long-lived, nonperturbative bipartite discrete time crystals in periodically driven quantum Ising models, revealing a rich prethermal phase diagram and stability to imperfections.

Contribution

It introduces the concept of bipartite discrete time crystals and analyzes their stability and phase structure using tensor network methods.

Findings

Exponential long-lived subharmonic response in the thermodynamic limit

Bipartite time-crystalline order stable to field imperfections

Rich prethermal phase diagram with multiple phases

Abstract

We study prethermal time-crystalline order in periodically driven quantum Ising models on disorder-free decorated lattices. Using a tensor network ansatz for the state which reflects the geometry of a unit cell of the lattice, we show through finite entanglement scaling that the system has an exponentially long-lived subharmonic response in the thermodynamic limit, which decays nonperturbatively in deviations from a perfect periodic drive. The resulting prethermal discrete time crystal is not only stable to imperfections in the transverse field, but also exhibits a bipartite rigidity to generic perturbations in the longitudinal field. We call this state a bipartite discrete time crystal and reveal a rich prethermal phase diagram, including multiple regions of bipartite time-crystalline order, uniform time-crystalline order and thermalization, with boundaries depending delicately on the topology of the decorated lattice. Our results thus uncover a variety of time crystals which may be realized on current digital quantum processors and analog quantum simulators.