Hartree Fock and RPA studies of the Hubbard model

TL;DR

This paper uses Hartree-Fock and RPA methods to analyze the 2D Hubbard model, revealing phases like antiferromagnetism, Fermi liquid behavior, and unconventional regimes with spin-charge textures, resembling 1D Luttinger liquids.

Contribution

It provides a detailed analysis of the Hubbard model using approximate methods, highlighting new regimes and features near half filling.

Findings

Antiferromagnetic phase at half filling

Fermi liquid behavior at low densities

Unconventional spin-charge textures near half filling

Abstract

The applicability of the Hartree-Fock and random phase approximations to models of strongly correlated electrons is discussed. The 2D Hubbard model is analyzed. An antiferromagnetic phase (at half filling) and Fermi liquid behavior (at low electron densities) are found. In addition, the system shows an unconventional regime near half filling. It is characterized by the formation of spin and charge textures. Local magnetic moments and spin waves are also present, and the quasiparticle pole at the Fermi energy vanishes. The charge excitation spectrum is gapless. The overall features resemble those of the 1D Luttinger liquid.