Within the tensor network framework, the (positive) thermal density operator can be approximated by a double layer of infinite Projected Entangled Pair Operator (iPEPO) coupled via ancilla degrees of freedom. To investigate the thermal properties of the spin-1/2 Heisenberg model on the square lattice, we introduce a family of fully spin-$SU(2)$ and lattice-$C_{4v}$ symmetric on-site tensors (of bond dimensions $D=4$ or $D=7$) and a plaquette-based Trotter-Suzuki decomposition of the imaginary-time evolution operator. A variational optimization is performed on the plaquettes, using a full (for $D=4$) or simple (for $D=7$) environment obtained from the single-site Corner Transfer Matrix Renormalization Group fixed point. The method is benchmarked by a comparison to quantum Monte Carlo in the thermodynamic limit. Although the iPEPO spin correlation length starts to deviate from the exact exponential growth for inverse-temperature $\beta \gtrsim 2$, the behavior of various observables turns out to be quite accurate once plotted w.r.t the inverse correlation length. We also find that a direct $T=0$ variational energy optimization provides results in full agreement with the $\beta\rightarrow\infty$ limit of finite-temperature data, hence validating the imaginary-time evolution procedure. Extension of the method to frustrated models is described and preliminary results are shown.

中文翻译：

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自旋1/2海森堡反铁磁体在方格上的有限温度对称张量网络

在张量网络框架中，（正）热密度算子可以通过无限自由投影纠缠对算子（iPEPO）通过辅助自由度耦合来近似。为了研究正方形晶格上spin-1 / 2 Heisenberg模型的热性能，我们引入了一个完全自旋$ SU（2）$和点阵$ C_ {4v} $对称现场张量（键为维度$ D = 4 $或$ D = 7 $）和虚时演化算子的​​基于Plaquette的Trotter-Suzuki分解。使用从单站点“角点转移矩阵重整化组”固定点获得的完整（对于$ D = 4 $）或简单（对于$ D = 7 $）环境，对球拍进行变分优化。该方法通过在热力学极限方面与量子蒙特卡洛进行比较来进行基准测试。尽管iPEPO自旋相关长度开始偏离逆温度$ \ beta \ gtrsim 2 $的确切指数增长，但是一旦绘制了逆相关长度，各种可观察对象的行为就变得非常准确。我们还发现直接$ T = 0 $变分能量优化可提供与有限温度数据的$ \ beta \ rightarrow \ infty $限制完全一致的结果，从而验证了虚时演化过程。描述了将该方法扩展到受挫模型，并显示了初步结果。我们还发现直接$ T = 0 $变分能量优化可提供与有限温度数据的$ \ beta \ rightarrow \ infty $限制完全一致的结果，从而验证了虚时演化过程。描述了将该方法扩展到受挫模型，并显示了初步结果。我们还发现直接$ T = 0 $变分能量优化可提供与有限温度数据的$ \ beta \ rightarrow \ infty $限制完全一致的结果，从而验证了虚时演化过程。描述了将该方法扩展到受挫模型，并显示了初步结果。