具有指数衰减相互作用的Lieb-Liniger模型：连续矩阵乘积态研究
Lieb-Liniger model with exponentially-decaying interactions: a continuous matrix product state study
摘要：
Lieb-Liniger模型描述了一维玻色子通过排斥接触势相互作用。在这项工作中，我们引入了一个扩展版本的这个模型，通过用衰减指数代替接触电位。利用最近发展起来的连续矩阵乘积态技术，我们通过考察超流和密度关联函数来探索该模型的基态相图。在弱耦合下，超流性支配着基态，其方式与Lieb-Liniger模型中的相似。然而，在强耦合准晶体和超Tonks Girardeau制度也被发现，这是不存在于原来的Lieb-Liniger的情况下。因此，指数衰减势的存在导致超流体/超Tonks Girardeau/准晶体交叉，当调谐耦合强度从弱到强相互作用。这对应于范围为$K \in (0, \infty)$的Luttinger液体参数;与Lieb-Liniger模型（其中为$K \in [1, \infty)$）和筛选的远程势（其中为$K \in (0, 1]$）形成鲜明对比。
英文摘要：
The Lieb-Liniger model describes one-dimensional bosons interacting through a repulsive contact potential. In this work, we introduce an extended version of this model by replacing the contact potential with a decaying exponential. Using the recently developed continuous matrix product states techniques, we explore the ground state phase diagram of this model by examining the superfluid and density correlation functions. At weak coupling superfluidity governs the ground state, in a similar way as in the Lieb-Liniger model. However, at strong coupling quasi-crystal and super-Tonks-Girardeau regimes are also found, which are not present in the original Lieb-Liniger case. Therefore the presence of the exponentially-decaying potential leads to a superfluid/super-Tonks-Girardeau/quasi-crystal crossover, when tuning the coupling strength from weak to strong interactions. This corresponds to a Luttinger liquid parameter in the range $K \in (0, \infty)$; in contrast with the Lieb-Liniger model, where $K \in [1, \infty)$, and the screened long-range potential, where $K \in (0, 1]$.
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