Imaginary time crystal of thermal quantum matter

Abstract

Temperature is a fundamental thermodynamic variable for matter. Physical observables are often found to either increase or decrease with it, or show a non-monotonic dependence with peaks signaling underlying phase transitions or anomalies. Statistical field theory has established connection between temperature and time: a quantum ensemble with inverse temperature β is formally equivalent to a dynamic system evolving along an imaginary time from 0 to iβ in the space one dimension higher. Here we report that a gas of hard-core bosons interacting with a thermal bath manifests an unexpected temperature-periodic oscillation of its macroscopic observables, arising from the microscopic origin of space-time locked translational symmetry breaking and crystalline ordering. Such a temperature crystal, supported by Quantum Monte Carlo simulation, generalizes the concept of purely spatial density-wave order by mapping the time axis for Euclidean action to an extra space dimension for free energy.

Discrete Time Crystals

“…In addition to the MBL and prethermal time crystals described in Section IV, there are a number of other strategies to impede thermalization. In the context of these alternate strategies, there has recently been an explosion of both theoretical proposals and experiments in the broad landscape surrounding time crystals [44,[90][91][92][93][94][95][96][97][98][99][100][101]. In this section, we will focus on summarizing this zoology (Fig.…”