论文标题
在2D经典硬杆模型的相变处的纠缠熵的对数差异不存在
Absence of logarithmic divergence of the entanglement entropies at the phase transitions of a 2D classical hard rod model
论文作者
论文摘要
纠缠熵是检测量子和经典系统中连续，不连续甚至拓扑相变的强大工具。在这项工作中，对正方形几何形状中的经典晶格模型进行了数值研究，冯·诺伊曼（Von Neumann）和雷尼（Renyi）纠缠熵进行了研究。从广场的中心到其中一个边缘的中点（例如右边缘）进行切割。纠缠熵测量系统的左侧和右半之间的纠缠。就像在剥离几何形状中一样，冯·诺伊曼（Von Neumann）和雷尼（Renyi）的纠缠熵在过渡点上对数分歧，而它们显示出一阶相变的跳跃。该分析扩展到沉积在平方晶格上的非重叠有限硬杆的经典模型，蒙特卡洛模拟表明，当硬杆跨越了7个或更多的晶格位点时，在两个无序相之间的相图中出现了列中相。引入了一种新的角传递矩阵重归于算法（CTMRG）来研究该模型。在此处讨论的CTMRG计算中的相变处，未观察到纠缠熵的对数差异。因此，我们推断出过渡既不能属于文献中的伊辛普遍性类别，也不是不连续的。
Entanglement entropy is a powerful tool to detect continuous, discontinuous and even topological phase transitions in quantum as well as classical systems. In this work, von Neumann and Renyi entanglement entropies are studied numerically for classical lattice models in a square geometry. A cut is made from the center of the square to the midpoint of one of its edges, say the right edge. The entanglement entropies measure the entanglement between the left and right halves of the system. As in the strip geometry, von Neumann and Renyi entanglement entropies diverge logarithmically at the transition point while they display a jump for first-order phase transitions. The analysis is extended to a classical model of non-overlapping finite hard rods deposited on a square lattice for which Monte Carlo simulations have shown that, when the hard rods span over 7 or more lattice sites, a nematic phase appears in the phase diagram between two disordered phases. A new Corner Transfer Matrix Renormalization Group algorithm (CTMRG) is introduced to study this model. No logarithmic divergence of entanglement entropies is observed at the phase transitions in the CTMRG calculation discussed here. We therefore infer that the transitions neither can belong to the Ising universality class, as previously assumed in the literature, nor be discontinuous.
