Performance of the rigorous renormalization group for first-order phase transitions and topological phases
Performance of the rigorous renormalization group for first-order phase transitions and topological phases
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DOI：
10.1103/physrevb.103.195122
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发表时间：
2020-10
影响因子：
3.7
通讯作者：
M. Block;J. Motruk;S. Gazit;M. Zaletel;Zeph Landau;U. Vazirani;N. Yao
中科院分区：
文献类型：
--
作者：
M. Block;J. Motruk;S. Gazit;M. Zaletel;Zeph Landau;U. Vazirani;N. Yao
扩展和改进用于研究量子晶格模型的数值方法是多体物理中的一个持续关注的焦点。虽然密度矩阵重整化群(DMRG)已被建立为一维系统中寻找基态的实用算法，但在Landau等人引入严格的重整化群(RRG)之前，一直没有一个被证明有效和准确的算法。[自然物理学11,566(2015)]。本文研究了RRG在一阶相变和对称保护拓扑相的数值实现的精度和性能。我们研究的动机是RRG何时可能为更成熟的DMRG技术提供有用的补充。特别是，尽管DMRG具有普遍的实用性，但它在一阶相变附近和拓扑相给出的结果是不可靠的，因为它的局部更新过程不能充分探索(近)退化流形。与此同时，RRG的严谨理论基础表明，它不应遭遇同样的困难。我们证明这种乐观是合理的，并且RRG确实确定了准确的、有序的能量，即使DMRG不确定。此外，我们的性能分析表明，在某些情况下，使用由RRG的粗略游程确定的状态来播种DMRG可能比简单地执行DMRG具有优势。
Expanding and improving the repertoire of numerical methods for studying quantum lattice models is an ongoing focus in many-body physics. While the density matrix renormalization group (DMRG) has been established as a practically useful algorithm for finding the ground state in 1D systems, a provably efficient and accurate algorithm remained elusive until the introduction of the rigorous renormalization group (RRG) by Landau et al. [Nature Physics 11, 566 (2015)]. In this paper, we study the accuracy and performance of a numerical implementation of RRG at first order phase transitions and in symmetry protected topological phases. Our study is motived by the question of when RRG might provide a useful complement to the more established DMRG technique. In particular, despite its general utility, DMRG can give unreliable results near first order phase transitions and in topological phases, since its local update procedure can fail to adequately explore (near) degenerate manifolds. The rigorous theoretical underpinnings of RRG, meanwhile, suggest that it should not suffer from the same difficulties. We show this optimism is justified, and that RRG indeed determines accurate, well-ordered energies even when DMRG does not. Moreover, our performance analysis indicates that in certain circumstances seeding DMRG with states determined by coarse runs of RRG may provide an advantage over simply performing DMRG.