Density-matrix renormalization-group method in momentum space

TL;DR

This paper introduces a momentum-space DMRG method for studying the Hubbard model, demonstrating its accuracy and usefulness in calculating ground state energies in two-dimensional systems, including larger lattices.

Contribution

The paper develops a momentum-space DMRG approach and shows its effectiveness in accurately computing ground state energies of the Hubbard model in two dimensions.

Findings

Accurately reproduces ground state energies on 4x4 lattices.

Provides new upper bounds for 8x8 lattice energies.

Shows the method's usefulness for fundamental models of interacting electrons.

Abstract

A momentum-space approach of the density-matrix renormalization-group (DMRG) method is developed. Ground state energies of the Hubbard model are evaluated using this method and compared with exact diagonalization as well as quantum Monte-Carlo results. It is shown that the momentum-space DMRG is a very useful numerical tool for studying the Hubbard model and other fundamental models of interacting electrons in two dimensions. For the Hubbard model in two dimensions, the momentum-space DMRG method reproduces accurately the exact diagonalization results of ground state energies on a $4\times 4$ lattice and yields new upper bounds of ground state energies on an 8$\times$8 lattice.