Multi-reference symmetry-projected variational approaches for ground and excited states of the one-dimensional Hubbard model

TL;DR

This paper introduces a multi-reference symmetry-projected variational method for accurately describing ground and excited states of the one-dimensional Hubbard model, matching exact solutions and providing detailed spectral and correlation data.

Contribution

The work develops a novel symmetry-projected configuration mixing approach that effectively captures correlations in the 1D Hubbard model, improving upon existing approximations.

Findings

Results agree well with exact Lieb-Wu solutions for lattices up to 50 sites.

Spectral functions and density of states are accurately computed.

Intrinsic symmetry-broken determinants reveal rich quantum fluctuation structures.

Abstract

We present a multi-reference configuration mixing scheme for describing ground and excited states, with well defined spin and space group symmetry quantum numbers, of the one-dimensional Hubbard model with nearest-neighbor hopping and periodic boundary conditions. Within this scheme, each state is expanded in terms of non-orthogonal and variationally determined symmetry-projected configurations. The results for lattices up to 30 and 50 sites compare well with the exact Lieb-Wu solutions as well as with results from other state-of-the-art approximations. In addition to spin-spin correlation functions in real space and magnetic structure factors, we present results for spectral functions and density of states computed with an ansatz whose quality can be well-controlled by the number of symmetry-projected configurations used to approximate the systems with $N_{e}$ and $N_{e} \pm 1$ electrons. The intrinsic symmetry-broken determinants resulting from the variational calculations have rich structures in terms of defects that can be regarded as basic units of quantum fluctuations. Given the quality of the results here reported, as well as the parallelization properties of the considered scheme, we believe that symmetry-projection techniques, which have found ample applications in nuclear structure physics, deserve further attention in the study of low-dimensional correlated many-electron systems.