强关联电子体系的量子蒙特卡罗计算

理解强关联电子体系是一个长期的重要目标,该体系的魅力不仅在于其背后蕴藏着深刻的物理,还在于其中涌现出的丰富物质态在量子调控、量子计算等领域具有巨大的潜在应用价值.同时,理论上非微扰地理解强关联电子体系是极其困难的,一直充满挑战.量子蒙特卡罗计算是一类非微扰计算的标准方法,有助于对强关联电子体系提供非微扰的理解,因而广泛运用于凝聚态和高能物理领域.然而,量子蒙特卡罗计算通常会受到负符号问题的困扰.本文将具体介绍一些无负符号关联电子模型的设计思路,并讨论我们近期提出的符号边界理论.通过设计无负符号或者具有代数符号行为的强关联电子模型,可以帮助人们研究很多重要的量子多体问题,包括巡游磁性量子临界行为、非常规超导和磁性序的竞争,以及莫尔(moiré)量子物质中的关联物相与相变等.     

Correlated insulating phases in the twisted bilayer graphene

We review analytical and numerical studies of correlated insulating states in twisted bilayer graphene, focusing on real-space lattice models constructions and their unbiased quantum many-body solutions. We show that by constructing localized Wannier states for the narrow bands, the projected Coulomb interactions can be approximated by interactions of cluster charges with assisted nearest neighbor hopping terms. With the interaction part only, the Hamiltonian is SU(4)symmetric considering both spin and valley degrees of freedom. In the strong coupling limit where the kinetic terms are neglected, the ground states are found to be in the SU(4) manifold with degeneracy. The kinetic terms, treated as perturbation, break this large SU(4) symmetry and propel the appearance of intervalley coherent state, quantum topological insulators, and other symmetry-breaking insulating states. We first present the theoretical analysis of moiré lattice model construction and then show how to solve the model with large-scale quantum Monte Carlo simulations in an unbiased manner. We further provide potential directions such that from the real-space model construction and its quantum many-body solutions how the perplexing yet exciting experimental discoveries in the correlation physics of twisted bilayer graphene can be gradually understood. This review will be helpful for the readers to grasp the fast growing field of the model study of twisted bilayer graphene.     

Band gap anomaly and topological properties in lead chalcogenides

Band gap anomaly is a well-known issue in lead chalcogenides Pb X(X = S, Se, Te, Po). Combining ab initio calculations and tight-binding(TB) method, we have studied the band evolution in Pb X, and found that the band gap anomaly in Pb Te is mainly related to the high on-site energy of Te 5s orbital and the large s–p hopping originated from the irregular extended distribution of Te 5s electrons. Furthermore, our calculations show that Pb Po is an indirect band gap(6.5 me V) semiconductor with band inversion at L point, which clearly indicates that Pb Po is a topological crystalline insulator(TCI). The calculated mirror Chern number and surface states double confirm this conclusion.