Symmetry-projected variational approach for ground and excited states of the two-dimensional Hubbard model

TL;DR

This paper introduces a symmetry-projected variational method for accurately computing ground and excited states of the 2D Hubbard model, demonstrating good agreement with exact and advanced numerical results across various lattice sizes.

Contribution

It develops a symmetry-projected configuration mixing scheme for the 2D Hubbard model, providing a computationally efficient approach with high accuracy for ground and excited states.

Findings

Results agree well with exact and other advanced methods.

Spectral functions and density of states are accurately obtained.

Method is computationally low-cost and effective for various lattice sizes.

Abstract

We present a symmetry-projected configuration mixing scheme to describe ground and excited states, with well defined quantum numbers, of the two-dimensional Hubbard model with nearestneighbor hopping and periodic boundary conditions. Results for the half-filled 2{\times}4, 4{\times}4, and 6{\times}6 lattices, as well as doped 4 {\times} 4 systems, compare well with available results, both exact and from other state-of-the-art approximations. We report spectral functions and density of states obtained from a well-controlled ansatz for the (Ne {\pm} 1)-electron system. Symmetry projected methods have been widely used for the many-body nuclear physics problem but have received little attention in the solid state community. Given their relatively low (mean-field) computational cost and the high quality of results here reported, we believe that they deserve further scrutiny.