论文标题
基准为全球$ su（2）$对称性在2D张量网络算法中
Benchmarking global $SU(2)$ symmetry in 2d tensor network algorithms
论文作者
论文摘要
我们在两个空间维度和热力学限制中以$ su（2）$对称的系统实现和基准测试张量网络算法。具体而言，我们实施了$ su（2）$ - 无限投影纠缠对状态（IPEP）和无限投影纠缠的单纯形状态（IPESS）方法的不变版本。我们对$ su（2）$对称的实施遵循[P.的融合树的形式主义Schmoll，S。Singh，M。Rizzi，R。Orús，Arxiv：1809.08180]。为了评估实施$ su（2）$对称性的实用性，对具有不同局部旋转的三种型号进行了基准测试：方形晶格上的spin-1 bilinear-biquadratic模型，以及Kagome Heisenberg Heisenberg Antiferromagnets（KHAF），用于Spin-1/2和Spin-2和Spin-2。我们观察到，$ su（2）$对称性的实现总体上比非对称模拟提供了更好的能量，相对于ANSATZ中参数的数量，尺度平滑，并且取决于模型的细节。特别是，对于Spin-2 KHAF模型，我们的$ SU（2）$模拟与量子自旋液态基态兼容。
We implement and benchmark tensor network algorithms with $SU(2)$ symmetry for systems in two spatial dimensions and in the thermodynamic limit. Specifically, we implement $SU(2)$-invariant versions of the infinite Projected Entangled Pair States (iPEPS) and infinite Projected Entangled Simplex States (iPESS) methods. Our implementation of $SU(2)$ symmetry follows the formalism based on fusion trees from [P. Schmoll, S. Singh, M. Rizzi, R. Orús, arXiv:1809.08180]. In order to assess the utility of implementing $SU(2)$ symmetry the algorithms are benchmarked for three models with different local spin: the spin-1 bilinear-biquadratic model on the square lattice, and the Kagome Heisenberg antiferromagnets (KHAF) for spin-1/2 and spin-2. We observe that the implementation of $SU(2)$ symmetry provides better energies in general than non-symmetric simulations, with smooth scalings with respect to the number of parameters in the ansatz, and with the actual improvement depending on the specifics of the model. In particular, for the spin-2 KHAF model, our $SU(2)$ simulations are compatible with a quantum spin liquid ground state.
