A Renormalization Group Method for Quasi One-dimensional Quantum Hamiltonians

Abstract

A density-matrix renormalization group (DMRG) method for highly anisotropic two-dimensional systems is presented. The method consists in applying the usual DMRG in two steps. In the first step, a pure one dimensional calculation along the longitudinal direction is made in order to generate a low energy Hamiltonian. In the second step, the anisotropic 2D lattice is obtained by coupling in the transverse direction the 1D Hamiltonians. The method is applied to the anisotropic quantum spin half Heisenberg model on a square lattice.

4 pages, 4 figures

References in corpus (10)

• Resonating Valence Bond Theory of Coupled Heisenberg Chains
• Density matrix algorithm for the calculation of dynamical properties of low dimensional systems
• Spin Gaps in a Frustrated Heisenberg model for CaV${}_4$O${}_9$
• Density-matrix renormalization-group method in momentum space
• Density Matrix Approach to Local Hilbert Space Reduction
• Density Matrix Renormalization Group Applied to the Ground State of the XY-Spin-Peierls System
• Calculation of the singlet-triplet gap of the antiferromagnetic Heisenberg Model on the ladder
• Ground-state properties of the One-dimensional Kondo Lattice at partial Band-filling
• Thermodynamic Density Matrix renormalization Group Study of the Magnetic Susceptibility of Half-integer Quantum Spin Chains
• Temperature-induced gap formation in dynamic correlation functions of the one-dimensional Kondo insulator --- Finite-temperature density-matrix renormalization-group study ---

Cited by in corpus (8)

• The density-matrix renormalization group
• New Trends in Density Matrix Renormalization
• Renormalization group method for weakly-coupled quantum chains: application to the spin one-half Heisenberg model
• Density Matrix Renormalisation Group Calculations for Two-Dimensional Lattices: An Application to the Spin-Half and Spin-One Square-Lattice Heisenberg Models
• Disordered phase of a two-dimensional Heisenberg Model with S=1
• Néel and disordered phases of coupled Heisenberg chains with $S=1/2$ to S=4
• A Matrix Kato-Bloch Perturbation Method for Hamiltonian Systems
• An Improved Initialization Procedure for the Density-Matrix Renormalization Group