Gradient optimization of finite projected entangled pair states
Gradient optimization of finite projected entangled pair states
复制标题
有限投影纠缠对态的梯度优化
DOI：
10.1103/physrevb.95.195154
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发表时间：
2016-11
影响因子：
3.7
通讯作者：
He Lixin
中科院分区：
文献类型：
--
作者：
Liu Wen-Yuan;Dong Shao-Jun;Han Yong-Jian;Guo Guang-Can;He Lixin
投影纠缠对态（PEPS）方法已被证明是解决二维强关联量子多体问题的有力工具。然而，由于高计算缩放与虚拟键尺寸$D$，在实际应用中，PEPS往往被限制到相当小的键尺寸，这可能是不够大的一些高度纠缠的系统，例如，挫折系统。采用时间演化方法和简单的更新方案对基态进行优化，可以得到更大的键维。然而，局部张量的环境的粗糙近似的准确性是值得怀疑的。在这里，我们表明，结合时间演化方法与简单的更新，蒙特卡罗采样技术和梯度优化将提供一个有效的方法来计算PEPS基态。利用大规模并行计算的优势，我们可以研究具有更大键维数的量子系统，直到$D$=10，而不诉诸任何对称性。在J_1 $-J_2 $模型上进行的基准测试表明，该方法的精度与精确结果相比令人印象深刻。
The projected entangled pair states (PEPS) methods have been proved to be powerful tools to solve the strongly correlated quantum many-body problems in two-dimension. However, due to the high computational scaling with the virtual bond dimension $D$, in a practical application PEPS are often limited to rather small bond dimensions, which may not be large enough for some highly entangled systems, for instance, the frustrated systems. The optimization of the ground state using time evolution method with simple update scheme may go to a larger bond dimension. However, the accuracy of the rough approximation to the environment of the local tensors is questionable. Here, we demonstrate that combining the time evolution method with simple update, Monte Carlo sampling techniques and gradient optimization will offer an efficient method to calculate the PEPS ground state. By taking the advantages of massive parallel computing, we can study the quantum systems with larger bond dimensions up to $D$=10 without resorting to any symmetry. Benchmark tests of the method on the $J_1$-$J_2$ model give impressive accuracy compared with exact results.