标题： 一维玻色-哈伯德模型中的再进入和纠缠 显示英文标题

标题： Re-entrance and entanglement in the one-dimensional Bose-Hubbard model

摘要： 再进入是一种新特性，其中系统的相边界在仅改变一个参数时表现出A相和B相之间的连续转变，如A-B-A-B，当仅一个参数单调变化时。这种类型的再进入出现在一维玻色-哈伯德模型中，在跃迁幅度从零增加时，其莫特绝缘体（MI）相和超流相之间显示这种现象。在这里，我们通过利用无限时间演化块消去算法，在热力学极限下直接分析这一反直觉现象，以变分方式最小化由矩阵大小chi参数化的无限矩阵乘积态（MPS）。利用固定chi对半链纠缠的直接限制，我们确定再进入仅在chi >= 8时在此近似情况下出现。这个纠缠阈值被发现与无限MPS同时具有粒子数对称性并捕捉到MI之上的粒子-空穴激发所携带的动能的能力一致。聚焦于MI瓣的尖端，我们首次对该处存在的无限阶Kosterlitz-Thouless临界点进行了通用的有限纠缠标度分析。通过分析到相当适中的chi = 70，我们得到了KT转变t_KT = 0.30 +/- 0.01的估计值，证明了有限纠缠方法不仅可以提供定性见解，还可以提供定量准确的预测。 显示英文摘要

摘要： Re-entrance is a novel feature where the phase boundaries of a system exhibit a succession of transitions between two phases A and B, like A-B-A-B, when just one parameter is varied monotonically. This type of re-entrance is displayed by the 1D Bose Hubbard model between its Mott insulator (MI) and superfluid phase as the hopping amplitude is increased from zero. Here we analyse this counter-intuitive phenomenon directly in the thermodynamic limit by utilizing the infinite time-evolving block decimation algorithm to variationally minimize an infinite matrix product state (MPS) parameterized by a matrix size chi. Exploiting the direct restriction on the half-chain entanglement imposed by fixing chi, we determined that re-entrance in the MI lobes only emerges in this approximate when chi >= 8. This entanglement threshold is found to be coincident with the ability an infinite MPS to be simultaneously particle-number symmetric and capture the kinetic energy carried by particle-hole excitations above the MI. Focussing on the tip of the MI lobe we then applied, for the first time, a general finite-entanglement scaling analysis of the infinite order Kosterlitz-Thouless critical point located there. By analysing chi's up to a very moderate chi = 70 we obtained an estimate of the KT transition as t_KT = 0.30 +/- 0.01, demonstrating the how a finite-entanglement approach can provide not only qualitative insight but also quantitatively accurate predictions.