两腿XXZ自旋梯子模型的量子相变与量子临界现象
Quantum phase transition and quantum critical phenomena in a spin-1/2 two-leg XXZ spin ladder model

对于限大尺寸两腿自旋1/2的XXZ自旋梯子模型,通过运用基于随机行走的张量网络（TN）算法数值模拟出基态波函数,尝试研究自旋梯子模型的约化保真度、普适序参量、纠缠熵等物理观测量,并系统研究基态保真度的三维挤点与二维分叉、约化保真度的分叉、局域序参量、普适序参量、纠缠熵和量子相变之间存在的关联关系.基于张量网络表示的算法在任意随机选择初始状态时,可以得到两腿XXZ量子自旋梯子系统简并的对称破缺基态波函数,该基态波函数是由于Z2对称破缺引起的.本文期望所提供的方法可为进一步研究凝聚态物质中热力学极限下的强关联电子量子晶格自旋梯子系统的量子相变和量子临界现象提供一种更有效的强大的工具.
In this study, a spin-1/2 two-leg XXZ spin ladder model with a double coupled infinite-size ladder system is systematically studied in terms of a tensor network (TN) algorithm. The algorithm is based on the tensor network representation of quantum many-body states, as an adaptation of the projected entangled pair states to the geometry of translationally invariant infinite-size quantum spin ladders. The TN algorithm provides an effective method by which to generate degenerate symmetry-breaking ground-state wave functions arising from the symmetry breaking, each of which results from a randomly chosen initial state. At the same time, we have also investigated an intriguing connection among fidelity per lattice site, reduced fidelity, local order parameter, universal order parameter, entropy and quantum phase transitions in the ground-state for the quantum two-leg XXZ model. The ground-state phase diagram of the ladder model exhibits a rich diversity of quantum phases. We expect that this approach may provide further insights into critical phenomena in quantum many-body lattice systems of condensed matter.