标题： 约束的对称化——受限晶格模型的密度矩阵重正化群 显示英文标题

标题： Symmetrizing the Constraints -- Density Matrix Renormalization Group for Constrained Lattice Models

摘要： 我们开发了一种密度矩阵重正化群（DMRG）算法，用于受限的量子晶格模型，该算法成功实现了{\it{在矩阵乘积态和矩阵乘积算符的收缩中实现局部约束作为对称性}}。 这种实现使我们能够用DMRG研究任意缠绕在具有相当周长的圆柱上的晶格几何结构上的量子二聚模型。 因此，我们计算了三角晶格上量子二聚模型的基态相图，完全捕捉到了柱状固相和$\sqrt{12}\times\sqrt{12}$价键固相的对称性破缺特性，以及扩展到非双部分晶格RK点上的$\mathbb{Z}_2$量子自旋液体相的拓扑纠缠熵。 我们针对受限量子晶格模型的DMRG算法为这些系统的基于矩阵和张量的算法开辟了新的机会，这与受挫量子磁体和合成量子模拟器有直接的相关性。 显示英文摘要

摘要： We develop a density matrix renormalization group (DMRG) algorithm for constrained quantum lattice models that successfully {\it{implements the local constraints as symmetries in the contraction of the matrix product states and matrix product operators}}. Such an implementation allows us to investigate a quantum dimer model in DMRG for any lattice geometry wrapped around a cylinder with substantial circumference. We have thence computed the ground state phase diagram of the quantum dimer model on triangular lattice, with the symmetry-breaking characteristics of the columnar solid phase and $\sqrt{12}\times\sqrt{12}$ valence bond solid phase fully captured, as well as the topological entanglement entropy of the $\mathbb{Z}_2$ quantum spin liquid phase that extends to the RK point on non-bipartite lattice accurately revealed. Our DMRG algorithm on constrained quantum lattice models opens new opportunities for matrix and tensor-based algorithms for these systems that have immediate relevance towards the frustrated quantum magnets and synthetic quantum simulators.