Ising Expansion for the Hubbard Model

TL;DR

This paper introduces a series expansion method using Ising anisotropy to analyze the ground state properties of the 2D Hubbard model, revealing a crossover in magnetic behavior and comparing results with other computational approaches.

Contribution

It presents a novel series expansion technique for the Hubbard model based on Ising anisotropy, providing detailed ground state property calculations.

Findings

Identifies a crossover around U≈4 between different antiferromagnetic regimes.

Calculates ground state energy, local moment, and other properties as functions of U/t.

Shows good agreement with Monte Carlo, RPA, and mean field results.

Abstract

We develop series expansions for the ground state properties of the Hubbard model, by introducing an Ising anisotropy into the Hamiltonian. For the two-dimensional (2D) square lattice half-filled Hubbard model, the ground state energy, local moment, sublattice magnetization, uniform magnetic susceptibility and spin stiffness are calculated as a function of $U/t$, where $U$ is the Coulomb constant and $t$ is the hopping parameter. Magnetic susceptibility data indicate a crossover around $U\approx 4$ between spin density wave antiferromagnetism and Heisenberg antiferromagnetism. Comparisons with Monte Carlo simulations, RPA result and mean field solutions are also made.