Spontaneous symmetry breaking is responsible for rich quantum phenomena from crystalline structures to superconductivity. This concept was boldly extended to the breaking of time translation, opening an avenue to finding exotic phases of quantum matter with collective time modulation and correlation. Here we report that a thermally open quantum ensemble manifests in the dual space of imaginary time with crystalline ordering due to a bath-induced retarded interaction. Exact quantum Monte Carlo simulations are performed to show that this imaginary time crystal phase exhibits characteristic ground-state and thermal properties absent in conventional quantum manybody systems, especially the striking temperature-oscillating behavior of its physical observables.

中文翻译：

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热量子物质的虚时间晶体

自发对称性破缺是导致从晶体结构到超导性的丰富量子现象的原因。这个概念被大胆地扩展到打破时间平移，为寻找具有集体时间调制和相关性的量子物质的奇异相开辟了道路。在这里，我们报告说，由于浴诱导的延迟相互作用，热开放量子系综出现在虚时间的双重空间中，具有晶体有序性。进行了精确的量子蒙特卡罗模拟，以表明这种假想时间晶相表现出传统量子多体系统中不存在的特征基态和热特性，尤其是其物理可观测物的显着温度振荡行为。