Spin density wave selection in the one-dimensional Hubbard model

TL;DR

This paper investigates the ground state phases of the one-dimensional Hubbard model using Hartree-Fock approximation, identifying various magnetic phases and their stability across different fillings.

Contribution

It provides a detailed phase diagram of the 1D Hubbard model constrained to uniform phases, including the identification of ferromagnetic, spiral, and double spin density wave states.

Findings

FM occurs at small filling

SSDW dominates most of the phase diagram

DSDW appears near quarter filling

Abstract

The Hartree-Fock ground state phase diagram of the one-dimensional Hubbard model is calculated, constrained to uniform phases, which have no charge density modulation. The allowed solutions are saturated ferromagnetism (FM), a spiral spin density wave (SSDW) and a double spin density wave} (DSDW). The DSDW phase comprises two canted interpenetrating antiferromagnetic sublattices. FM occurs for small filling, SSDW in most of the remainder of the phase diagram, and DSDW in a narrow tongue near quarter (and three-quarter) filling. Itinerant electrons lift the degeneracy with respect to canting angle in the DSDW. The Hartree-Fock states are metallic except at multiples of a quarter filling. Near half filling the uniform SSDW phase is unstable against phase separation into a half-filled antiferromagnetic phase and a hole-rich SSDW phase. The dependence of the ground state wave number on chemical potential is conjectured to be a staircase. Comparison is made with higher dimensional Hubbard models and the $J_{1}-J_{2}$ Heisenberg model.