Exploring the bulk-boundary correspondences and the boundary-induced phenomena in the strongly-correlated quantum systems belongs to the most fundamental topics of condensed matter physics. In this work, we study the bulk-boundary competition in a simulative Hamiltonian, with which the thermodynamic properties of the infinite-size translationally-invariant system can be optimally mimicked. The simulative Hamiltonian is constructed by introducing local interactions on the boundaries, coined as the entanglement-bath Hamiltonian (EBH) that is analogous to the heat bath. The terms within the EBH are variationally determined by a thermal tensor network method, with coefficients varying with the temperature of the infinite-size system. By treating the temperature as an adjustable hyper-parameter of the EBH, we identify a discontinuity point of the coefficients, dubbed as the ‘boundary quench point’ (BQP), whose physical implication is to distinguish the point, below which the thermal fluctuations from the boundaries to the bulk become insignificant. Fruitful phenomena are revealed when considering the simulative Hamiltonian, with the EBH featuring its own hyper-parameter, under the canonical ensembles at different temperatures. Specifically, a discontinuity in bulk entropy at the BQP is observed. The exotic entropic distribution, the relations between the symmetries of Hamiltonian and BQP, and the impacts from the entanglement-bath dimension are also explored. Our results show that such a singularity differs from those in the conventional thermodynamic phase transition points that normally fall into the Landau–Ginzburg paradigm. Our work provides the opportunities on exploring the exotic phenomena induced by the competition between the bulk and boundaries.

中文翻译：

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有限温度下强相关量子系统中的边界诱导奇点


探索强相关量子系统中的体边界对应关系和边界诱导现象属于凝聚态物理最基本的课题。在这项工作中，我们研究了模拟哈密顿量中的体边界竞争，从而可以最佳地模拟无限尺寸平移不变系统的热力学性质。模拟哈密顿量是通过在边界上引入局部相互作用来构建的，被称为纠缠浴哈密顿量（EBH），类似于热浴。 EBH 中的项由热张量网络方法可变地确定，系数随无限尺寸系统的温度而变化。通过将温度视为 EBH 的可调节超参数，我们确定了系数的不连续点，称为“边界淬火点”(BQP)，其物理含义是区分该点，低于该点的热波动来自主体的边界变得微不足道。当考虑模拟哈密顿量时，在不同温度下的规范系综下，EBH 具有自己的超参数，结果显示出富有成果的现象。具体来说，观察到 BQP 处体熵的不连续性。还探讨了奇异的熵分布、哈密顿量和 BQP 的对称性之间的关系以及纠缠浴维度的影响。我们的结果表明，这种奇点不同于通常属于朗道-金兹堡范式的传统热力学相变点。我们的工作提供了探索由体块和边界之间的竞争引起的奇异现象的机会。