探索二维量子晶格模型热力学性质的网络收缩动力学理论
Theory of Network Contractor Dynamics for Exploring Thermodynamic Properties of Two-dimensional Quantum Lattice Models
摘要：
基于张量网络态表象，我们发展了一个非线性动力学理论，称为网络收缩动力学（NCD），用来研究二维量子晶格模型的热力学性质。NCD方案通过调用多重线性代数中的秩- $1$分解，使得配分函数的张量网络的收缩通过一个边界上带有向量的局部张量簇的收缩来实现.本文提出了一种用于实际数值模拟的NCD方法的时间扫描算法。在平方伊辛模型上对NCD格式进行了基准检验，结果表明该格式具有很高的精度.此外，对蜂窝晶格上自旋为1/2的海森堡反铁磁体的计算结果与量子Monte Carlo计算结果符合得很好。在动力学方案中引入了准纠缠熵$S$、李雅普诺夫指数$I^{lya}$和回路特征$I^{loop}$，发现它们在临界点附近表现出“非定域性”，可用于确定经典和量子系统的热力学相变.
英文摘要：
Based on the tensor network state representation, we develop a nonlinear dynamic theory coined as network contractor dynamics (NCD) to explore the thermodynamic properties of two-dimensional quantum lattice models. By invoking the rank-$1$ decomposition in the multi-linear algebra, the NCD scheme makes the contraction of the tensor network of the partition function be realized through a contraction of a local tensor cluster with vectors on its boundary. An imaginary-time-sweep algorithm for implementation of the NCD method is proposed for practical numerical simulations. We benchmark the NCD scheme on the square Ising model, which shows a great accuracy. Besides, the results on the spin-1/2 Heisenberg antiferromagnet on honeycomb lattice are disclosed in good agreement with the quantum Monte Carlo calculations. The quasi-entanglement entropy $S$, Lyapunov exponent $I^{lya}$ and loop character $I^{loop}$ are introduced within the dynamic scheme, which are found to display the ``nonlocality" near the critical point, and can be applied to determine the thermodynamic phase transitions of both classical and quantum systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
