任意无限格的通用张量网络算法
A universal tensor network algorithm for any infinite lattice
摘要：
本文提出了一种基于图的投影纠缠对态（gPEPS）算法，用于计算任意无限大的格点或图上最近邻局域哈密顿量的基态。通过引入结构矩阵，它编码了任何维度$d$中任何图上的张量网络的细节，我们能够生成一个代码，该代码基本上可以用于模拟任何晶格。我们进一步引入了一个优化算法来计算简单的张量更新以及期望值和具有类似平均场的有效环境。虽然不是可变的，但该策略允许处理非常大的键尺寸的PEPS（例如，$D=100$），并且在许多情况下，特别是当关联长度小并且晶格的连接性大时，在热力学极限中产生非常精确的结果。我们证明了我们的方法的有效性，通过基准测试的算法对已知的结果为几个模型，即，链格、星格和立方格上的反铁磁海森堡模型，正方格上的硬核哈伯德模型，烧绿石格上的场铁磁海森堡模型，以及可果美格上的场$3$态量子Potts模型和三角格上的自旋- $1$双线性-双二次海森堡模型。通过研究正方晶格上横向磁场中$2d$量子伊辛模型的量子相变和超蜂窝晶格上Kitaev-Heisenberg模型的相图，进一步证明了gPEPS的性能.我们的结果与以前的研究非常一致。
英文摘要：
We present a general graph-based Projected Entangled-Pair State (gPEPS) algorithm to approximate ground states of nearest-neighbor local Hamiltonians on any lattice or graph of infinite size. By introducing the structural-matrix which codifies the details of tensor networks on any graphs in any dimension $d$, we are able to produce a code that can be essentially launched to simulate any lattice. We further introduce an optimized algorithm to compute simple tensor updates as well as expectation values and correlators with a mean-field-like effective environments. Though not being variational, this strategy allows to cope with PEPS of very large bond dimension (e.g., $D=100$), and produces remarkably accurate results in the thermodynamic limit in many situations, and specially when the correlation length is small and the connectivity of the lattice is large. We prove the validity of our approach by benchmarking the algorithm against known results for several models, i.e., the antiferromagnetic Heisenberg model on a chain, star and cubic lattices, the hardcore Bose-Hubbard model on square lattice, the ferromagnetic Heisenberg model in a field on the pyrochlore lattice, as well as the $3$-state quantum Potts model in field on the kagome lattice and the spin-$1$ bilinear-biquadratic Heisenberg model on the triangular lattice. We further demonstrate the performance of gPEPS by studying the quantum phase transition of the $2d$ quantum Ising model in transverse magnetic field on the square lattice, and the phase diagram of the Kitaev-Heisenberg model on the hyperhoneycomb lattice. Our results are in excellent agreement with previous studies.
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