Antiferromagnetic symmetry breaking in the half filled Hubbard model in infinite dimensions

TL;DR

This paper investigates antiferromagnetic symmetry breaking in the half-filled Hubbard model on an infinite-dimensional lattice, deriving exact identities and analyzing the accuracy of approximations for small interactions.

Contribution

It derives an exact Ward-identity for the model and demonstrates the accuracy of Hartree-Fock and RPA approximations in the weak coupling regime.

Findings

Long-range antiferromagnetic order develops at finite temperature.

Hartree-Fock and RPA are accurate for small U.

An exact Ward-identity relates vertex functions and self-energies.

Abstract

We study the half filled Hubbard model on a hypercubic lattice in infinite dimensions in the presence of a staggered magnetic field. An exact Ward-identity between vertex functions and self-energies is derived, that holds in any phase without broken symmetry for all values of $U$. Making the reasonable assumptions that for small enough on-site repulsion $U$ the high-temperature phase is a Fermi liquid, and that in the weak coupling regime the effective Anderson impurity model can be studied perturbatively, we proof that Hartree-Fock theory and the random-phase approximation are very accurate for small $U$, and that the system develops long-range antiferromagnetic order at a finite temperature.