论文标题
双曲线晶格几何形状上的量子自旋系统的区域法研究
Area-Law Study of Quantum Spin System on Hyperbolic Lattice Geometries
论文作者
论文摘要
通过张量产品变化公式研究了曲面（双曲线）晶格上横向场模型的磁性特性，我们为此目的进行了概括。首先，我们通过计算磁化化来确定每个双曲线晶格的量子相变。我们研究相变的纠缠熵，以分析中心位于中心的各个子系统与其他晶格的相关性。我们确认，纠缠熵满足固定配位数的相变处的区域定律，即，它随着子系统的大小增加而线性地缩放。另一方面，纠缠熵随着协调数的增加而降低。
Magnetic properties of the transverse-field Ising model on curved (hyperbolic) lattices are studied by a tensor product variational formulation that we have generalized for this purpose. First, we identify the quantum phase transition for each hyperbolic lattice by calculating the magnetization. We study the entanglement entropy at the phase transition in order to analyze the correlations of various subsystems located at the center with the rest of the lattice. We confirm that the entanglement entropy satisfies the area law at the phase transition for fixed coordination number, i.e., it scales linearly with the increasing size of the subsystems. On the other hand, the entanglement entropy decreases as power-law with respect to the increasing coordination number.
