论文标题
无限条带上的二维等距张量网络
Two Dimensional Isometric Tensor Networks on an Infinite Strip
论文作者
论文摘要
众所周知，通用二维（2D）张量网络状态（TNS）的确切收缩呈指数级，这使得对2D系统的模拟变得困难。最近引入的等距TNS（ISOTN）类别代表了TNS的子集，该子集允许在有限的方格上有效模拟此类系统。 ISOTNS ANSATZ需要识别张量的“正交列”，其中一维矩阵乘积状态（MPS）方法可用于计算可观察结果和张量的优化。在这里，我们将ISOTN扩展到无限长的带状几何形状，并引入了摩西移动算法的无限版本，用于移动网络周围的正交列。使用该算法，我们迭代地将2D量子态的无限MP表示为带状质量，并研究了所得状态的纠缠特性。此外，我们证明可以有效地评估局部可观察物。最后，我们介绍了无限的时间不断变化的块分解算法（itebd \ textsuperscript {2}），并使用它近似于无限条纹几何晶格的2D横向磁场模型的基态。
The exact contraction of a generic two-dimensional (2D) tensor network state (TNS) is known to be exponentially hard, making simulation of 2D systems difficult. The recently introduced class of isometric TNS (isoTNS) represents a subset of TNS that allows for efficient simulation of such systems on finite square lattices. The isoTNS ansatz requires the identification of an "orthogonality column" of tensors, within which one-dimensional matrix product state (MPS) methods can be used for calculation of observables and optimization of tensors. Here we extend isoTNS to infinitely long strip geometries and introduce an infinite version of the Moses Move algorithm for moving the orthogonality column around the network. Using this algorithm, we iteratively transform an infinite MPS representation of a 2D quantum state into a strip isoTNS and investigate the entanglement properties of the resulting state. In addition, we demonstrate that the local observables can be evaluated efficiently. Finally, we introduce an infinite time-evolving block decimation algorithm (iTEBD\textsuperscript{2}) and use it to approximate the ground state of the 2D transverse field Ising model on lattices of infinite strip geometry.
