Dulmage-Mendelsohn渗流：最大填充二聚体模型的几何结构与位点稀释二分格上拓扑保护的零模
Dulmage-Mendelsohn percolation: Geometry of maximally-packed dimer models and topologically-protected zero modes on site-diluted bipartite lattices
AI总结：
本研究通过Dulmage-Mendelsohn分解识别位点稀释二分格中局域子格失衡的单体承载区域，揭示其控制零能量子粒子局域化性质，发现Dulmage-Mendelsohn渗流普适类，且结果对多领域物理问题具有显著意义。
摘要：
经典组合结构“最大匹配”可探测位点稀释二分格中存在局域子格失衡的区域的随机几何特征。我们发现，这些承载格点任意最大匹配单体的区域，控制着零能量子粒子在该格点上跳跃的局域化性质。Dulmage和Mendelsohn的结构理论为我们提供了识别此类区域的完整且不重叠集合的方法，这推动了我们对二维和三维位点稀释二分格的Dulmage-Mendelsohn分解的大规模计算研究。我们的计算揭示了一个有趣的普适性渗流类，其与存在局域子格失衡的单体承载区域的端到端连通性相关，我们称之为“Dulmage-Mendelsohn渗流”。研究结果表明，相关最大填充二聚体模型的经典统计力学中存在单体渗流转变，对应量子二聚体模型的任意多体本征态存在面积律纠缠熵相；同时对Majorana模式局域于稀释格点上的二分网络的集体零能Majorana费米子激发性质、此类格点上二分随机跳跃问题的拓扑保护零能波函数特征（进而对相应量子渗流问题），以及少量非磁杂质稀释的二分量子反铁磁体的低能磁激发性质，均具有显著意义。
英文摘要：
The classic combinatorial construct of {\em maximum matchings} probes the random geometry of regions with local sublattice imbalance in a site-diluted bipartite lattice. We demonstrate that these regions, which host the monomers of any maximum matching of the lattice, control the localization properties of a zero-energy quantum particle hopping on this lattice. The structure theory of Dulmage and Mendelsohn provides us a way of identifying a complete and non-overlapping set of such regions. This motivates our large-scale computational study of the Dulmage-Mendelsohn decomposition of site-diluted bipartite lattices in two and three dimensions. Our computations uncover an interesting universality class of percolation associated with the end-to-end connectivity of such monomer-carrying regions with local sublattice imbalance, which we dub {\em Dulmage-Mendelsohn percolation}. Our results imply the existence of a monomer percolation transition in the classical statistical mechanics of the associated maximally-packed dimer model and the existence of a phase with area-law entanglement entropy of arbitrary many-body eigenstates of the corresponding quantum dimer model. They also have striking implications for the nature of collective zero-energy Majorana fermion excitations of bipartite networks of Majorana modes localized on sites of diluted lattices, for the character of topologically-protected zero-energy wavefunctions of the bipartite random hopping problem on such lattices, and thence for the corresponding quantum percolation problem, and for the nature of low-energy magnetic excitations in bipartite quantum antiferromagnets diluted by a small density of nonmagnetic impurities.
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