标题： 自旋-$\frac{1}{2}$ XXZ链在反铁磁间隙区域边界场下的完整边界相图 显示英文标题

标题： Complete Boundary Phase Diagram of the Spin-$\frac{1}{2}$ XXZ Chain with Boundary Fields in the Anti-Ferromagnetic Gapped Regime

摘要： 我们考虑具有对角边界场的自旋$\frac{1}{2}$XXZ 链，并在间隙反铁磁区域中使用贝特假设精确求解，得到完整的相变边界图。 根据边界场的值，系统表现出几种相，这些相可以根据系统表现出的基态以及根据局域于边界的束缚态数量进行分类。 我们表明，希尔伯特空间由一定数量的塔组成，其数量取决于系统表现出的边界束缚态数量。 当边界场跨越某些临界值时，系统会发生边界相变。 存在两种类型的相变。 在第一种类型中，系统的基态会发生变化。 在第二种类型中，称为“本征态相变”，希尔伯特空间的塔的数量会发生变化，这再次与系统表现出的边界束缚态数量的变化有关。 我们使用密度矩阵重正交化群（DMRG）和精确对角化技术，通过分析每个本征态中的自旋分布来探测本征态相变和基态相变的特征。 显示英文摘要

摘要： We consider the spin $\frac{1}{2}$ XXZ chain with diagonal boundary fields and solve it exactly using Bethe ansatz in the gapped anti-ferromagnetic regime and obtain the complete phase boundary diagram. Depending on the values of the boundary fields, the system exhibits several phases which can be categorized based on the ground state exhibited by the system and also based on the number of bound states localized at the boundaries. We show that the Hilbert space is comprised of a certain number of towers whose number depends on the number of boundary bound states exhibited by the system. The system undergoes boundary phase transitions when boundary fields are varied across certain critical values. There exist two types of phase transitions. In the first type the ground state of the system undergoes a change. In the second type, named the `Eigenstate phase transition', the number of towers of the Hilbert space changes, which is again associated with the change in the number of boundary bound states exhibited by the system. We use the DMRG and exact diagonalization techniques to probe the signature of the Eigenstate phase transition and the ground state phase transition by analyzing the spin profiles in each eigenstate.