Density Matrix Renormalization Group in Hybrid Momentum Space

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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.