Unifying projected entangled pair state contractions
Unifying projected entangled pair state contractions
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DOI：
10.1088/1367-2630/16/3/033014
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发表时间：
2013-11
影响因子：
3.3
通讯作者：
M. Lubasch;Ignacio Cirac;Mari-Carmen Ba˜nuls
中科院分区：
文献类型：
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作者：
M. Lubasch;Ignacio Cirac;Mari-Carmen Ba˜nuls
投影纠缠对态（PEPS）张量网络的近似收缩是任何PEPS算法的基本组成部分，需要在基态搜索或时间演化中优化张量，以及评估期望值。精确的压缩一般是不可能的，近似过程的选择决定了算法的效率和精度。我们分析了不同的以前的建议，这种近似，并表明，他们可以理解通过其环境的形式，即运营商的结果，从收缩网络的一部分。这提供了物理洞察各种方法的局限性，并允许我们引入一个新的策略，基于集群的想法，统一以前的方法。由此产生的收缩算法自然插值之间的最便宜的和最不精确的和最昂贵的和最精确的方法。我们用有限PEPS对不同的算法进行基准测试，并展示了集群策略如何用于张量优化和期望值的计算。此外，我们讨论了它的适用性PEPS的并行化和无限系统。
The approximate contraction of a tensor network of projected entangled pair states (PEPS) is a fundamental ingredient of any PEPS algorithm, required for the optimization of the tensors in ground state search or time evolution, as well as for the evaluation of expectation values. An exact contraction is in general impossible, and the choice of the approximating procedure determines the efficiency and accuracy of the algorithm. We analyze different previous proposals for this approximation, and show that they can be understood via the form of their environment, i.e. the operator that results from contracting part of the network. This provides physical insight into the limitation of various approaches, and allows us to introduce a new strategy, based on the idea of clusters, that unifies previous methods. The resulting contraction algorithm interpolates naturally between the cheapest and most imprecise and the most costly and most precise method. We benchmark the different algorithms with finite PEPS, and show how the cluster strategy can be used for both the tensor optimization and the calculation of expectation values. Additionally, we discuss its applicability to the parallelization of PEPS and to infinite systems.