改进的iPEPS算法：快速完全更新和规范固定
The iPEPS algorithm, improved: fast full update and gauge fixing
摘要：
无限投射纠缠对态（iPEPS）算法[J.Jordan等人，PRL 101，250602（2008）]已经成为在热力学极限中计算2d量子晶格系统的基态性质的有用工具。尽管它的许多成功的实现，该方法有一些限制，在其目前的配方，阻碍了它的应用到一些高度纠缠系统。本文的目的是解开其中的一些问题，从而提高iPEPS方法的稳定性和效率。为此，我们首先介绍快速完全更新方案，其中有效环境和iPEPS张量在整个时间内同时更新（或演化）。正如我们将展示的，这意味着两个关键的优势：（i）显著的计算节省，以及（ii）提高整体稳定性。此外，我们还扩展了\emph{local gauge fixing}的应用，成功地实现了有限大小的PEPS [M. Lubasch，J. C. Bañuls，PRB 90，064425（2014）]，到iPEPS算法。我们看到，规范固定不仅进一步提高了方法的稳定性，而且还加速了（“完整”或“快速完整”）张量更新方案中交替最小二乘扫描的收敛。通过研究无限正方形晶格上量子海森堡模型和横场伊辛模型的基态性质，对所得到的“改进的”iPEPS算法在计算成本和稳定性方面的改进进行了基准测试.
英文摘要：
The infinite Projected Entangled Pair States (iPEPS) algorithm [J. Jordan et al, PRL 101, 250602 (2008)] has become a useful tool in the calculation of ground state properties of 2d quantum lattice systems in the thermodynamic limit. Despite its many successful implementations, the method has some limitations in its present formulation which hinder its application to some highly-entangled systems. The purpose of this paper is to unravel some of these issues, in turn enhancing the stability and efficiency of iPEPS methods. For this, we first introduce the fast full update scheme, where effective environment and iPEPS tensors are both simultaneously updated (or evolved) throughout time. As we shall show, this implies two crucial advantages: (i) dramatic computational savings, and (ii) improved overall stability. Besides, we extend the application of the \emph{local gauge fixing}, successfully implemented for finite-size PEPS [M. Lubasch, J. Ignacio Cirac, M.-C. Bañuls, PRB 90, 064425 (2014)], to the iPEPS algorithm. We see that the gauge fixing not only further improves the stability of the method, but also accelerates the convergence of the alternating least squares sweeping in the (either "full" or "fast full") tensor update scheme. The improvement in terms of computational cost and stability of the resulting "improved" iPEPS algorithm is benchmarked by studying the ground state properties of the quantum Heisenberg and transverse-field Ising models on an infinite square lattice.
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