Understanding the stability of strongly correlated phases of matter when coupled to environmental degrees of freedom is crucial for identifying the conditions under which these states may be observed. Here, we focus on the paradigmatic one-dimensional Bose-Hubbard model, and study the stability of the Luttinger-liquid and Mott insulating phases in the presence of local particle exchange with site-independent baths of noninteracting bosons. We perform a numerically exact analysis of this model by adapting the recently developed wormhole quantum Monte Carlo method for retarded interactions to a continuous-time formulation with worm updates; we show how the wormhole updates can be easily implemented in this scheme. For an Ohmic bath, our numerical findings confirm the scaling prediction that the Luttinger-liquid phase becomes unstable at infinitesimal bath coupling. We show that the ensuing phase is a long-range-ordered superfluid with spontaneously broken U(1) symmetry. While the Mott insulator remains a distinct phase for small bath coupling, it exhibits diverging compressibility and noninteger local boson occupation in the thermodynamic limit. Upon increasing the bath coupling, this phase undergoes a transition to a long-range-ordered superfluid. Finally, we discuss the effects of super-Ohmic dissipation on the Luttinger-liquid phase. Our results are compatible with a stable dissipative Luttinger-liquid phase that transitions to a long-range-ordered superfluid at a finite system-bath coupling.

中文翻译：

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一维 Bose-Hubbard 模型中耗散引起的长程有序


了解强相关物质相与环境自由度耦合时的稳定性对于确定观察这些状态的条件至关重要。在这里，我们关注典型的一维 Bose-Hubbard 模型，并研究在与非相互作用玻色子的位置无关浴进行局部粒子交换的情况下 Luttinger 液体和莫特绝缘相的稳定性。我们通过将最近开发的用于延迟相互作用的虫洞量子蒙特卡罗方法改编为具有蠕虫更新的连续时间公式，对该模型进行了数值精确分析；我们展示了如何在此方案中轻松实现虫洞更新。对于欧姆浴，我们的数值结果证实了拉廷格液相在无穷小的浴耦合下变得不稳定的缩放预测。我们表明，随后的相是一种长程有序超流体，具有自发破缺的 U(1) 对称性。虽然莫特绝缘体仍然是小浴耦合的独特相，但它在热力学极限下表现出不同的压缩性和非整数局部玻色子占据。增加浴耦合后，该相转变为长程有序超流体。最后，我们讨论了超欧姆耗散对 Luttinger 液相的影响。我们的结果与稳定的耗散卢廷格液相兼容，该液相在有限系统浴耦合下转变为长程有序超流体。