Abstract

In the one-dimensional Bose-Hubbard model with on-site and nearest-neighbor interactions, a gapped phase characterized by an exotic non-local order parameter emerges, the Haldane insulator. Bose-Hubbard models with cavity-mediated global range interactions display phase diagrams, which are very similar to those with nearest-neighbor repulsive interactions, but the Haldane phase remains elusive there. Here we study the one-dimensional Bose-Hubbard model with nearest-neighbor and cavity-mediated global-range interactions and scrutinize the existence of a Haldane Insulator phase. With the help of extensive quantum Monte-Carlo simulations we find that in the Bose-Hubbard model with only cavity-mediated global-range interactions no Haldane phase exists. For a combination of both interactions, the Haldane Insulator phase shrinks rapidly with increasing strength of the cavity-mediated global-range interactions. Thus, in spite of the otherwise very similar behavior the mean-field like cavity-mediated interactions strongly suppress the non-local order favored by nearest-neighbor repulsion in some regions of the phase diagram.

Graphical abstract

中文翻译：

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一维最近邻扩展Bose-Hubbard模型中的Haldane绝缘子，具有腔介导的远程相互作用

摘要

在具有现场相互作用和最近邻相互作用的一维Bose-Hubbard模型中，出现了一个以奇异的非局部有序参数为特征的气隙相，即Haldane绝缘子。具有腔介导的全局范围相互作用的Bose-Hubbard模型显示的相图与具有最近邻排斥相互作用的相图非常相似，但Haldane相在那里仍然难以捉摸。在这里，我们研究一维Bose-Hubbard模型及其最近邻和腔介导的全局范围相互作用，并仔细研究Haldane绝缘子相的存在。借助广泛的量子蒙特卡洛模拟，我们发现在仅具有腔介导的全局范围相互作用的Bose-Hubbard模型中，不存在Haldane相。结合两种互动，Haldane绝缘体相随着腔介导的全球范围相互作用的强度增加而迅速收缩。因此，尽管在其他方面非常相似，但类似平均场的腔介导的相互作用在相图的某些区域中仍会强烈地抑制最近邻排斥所支持的非局部有序。

图形概要