Density Matrix Renormalization Group in Hybrid Momentum Space

这个项目的目标是用密度矩阵重整化群（DMRG）在混合动量空间表示中处理二维和多维的量子晶格模型。在二维中，混合动量空间表示在横向上使用动量空间表示，在纵向上使用实空间或其他局部表示，通常采用圆柱体几何形状。利用横向动量-空间量子数将大大提高二维系统的计算效率，并将允许对状态和可观测值的量子数进行更细粒度的控制。最初的应用领域将是二维哈伯德模型，其中长距离跳变和库仑排斥的扩展也将被处理。其他应用包括多波段哈伯德模型、受挫自旋模型、相互作用玻色子、量子霍尔系统和具有拓扑相的系统。

The objective of this project is to treat quantum lattice models in two and more dimensions within a hybrid momentum-space representation with the Density Matrix Renormalization Group (DMRG). In two dimensions, the hybrid momentum-space representation uses a momentum-space representation in the transverse direction and a real-space or other localized representation in the longitudinal direction, typically taking a cylinder geometry. Taking advantage of the transverse momentum-space quantum numbers will bring about a significant improvement in computational efficiency for two-dimensional systems and will allow finer-grained control of quantum numbers for states and observables. The initial area of application will be the two-dimensional Hubbard model, where the extensions of longer-range hopping and Coulomb repulsion will also be treated. Additional applications include multiple-band Hubbard models, frustrated spin models, interacting bosons, quantum Hall systems, and systems with topological phases.