Multiplicity, localization, and domains in the Hartree-Fock ground state of the two-dimensional Hubbard model

TL;DR

This paper investigates the Hartree-Fock approximation for the 2D Hubbard model, revealing a multitude of nearly degenerate solutions, their localization properties, and the emergence of stripe and domain structures at various interaction strengths.

Contribution

It uncovers the extensive multiplicity of Hartree-Fock solutions and analyzes their physical relevance, localization, and domain structures in the 2D Hubbard model.

Findings

Numerous nearly degenerate Hartree-Fock solutions exist.

Wavefunctions are unlocalized at small/moderate U/t, localized at high U/t.

Stripe and rectangular domain structures are observed.

Abstract

We explore certain properties of the Hartree-Fock approximation to the ground state of the two-dimensional Hubbard model, emphasizing the fact that in the Hartree approach there is an enormous multiplicity of self-consistent solutions which are nearly degenerate in energy, reminiscent of a spin glass, but which may differ substantially in other bulk properties. It is argued that this multiplicity is physically relevant at low temperatures. We study the localization properties of the one-particle wavefunctions comprising the Hartree-Fock states, and find that these are unlocalized at small and moderate values of U/t, in particular in the stripe region, but become highly localized at values corresponding to strong repulsion. We also find rectangular domains as well as stripes in the stripe region of the phase diagram, and study pair correlations in the neighborhood of half-filling.