Neel order, ring exchange and charge fluctuations in the half-filled Hubbard model

TL;DR

This paper studies the ground state of the half-filled 2D Hubbard model beyond the Heisenberg limit, revealing how charge fluctuations affect magnetic order and quantum fluctuations.

Contribution

It introduces an effective spin-only theory including higher-order interactions and analyzes the impact of charge fluctuations on the staggered magnetization in the Hubbard model.

Findings

Staggered magnetization decreases monotonically with t/U.

Charge fluctuations increase quantum fluctuations beyond the Heisenberg limit.

Renormalization factor accounts for charge fluctuation effects on the order parameter.

Abstract

We investigate the ground state properties of the two dimensional half-filled one band Hubbard model in the strong (large-U) to intermediate coupling limit ({\it i.e.} away from the strict Heisenberg limit) using an effective spin-only low-energy theory that includes nearest-neighbor exchange, ring exchange, and all other spin interactions to order t(t/U)^3. We show that the operator for the staggered magnetization, transformed for use in the effective theory, differs from that for the order parameter of the spin model by a renormalization factor accounting for the increased charge fluctuations as t/U is increased from the t/U -> 0 Heisenberg limit. These charge fluctuations lead to an increase of the quantum fluctuations over and above those for an S=1/2 antiferromagnet. The renormalization factor ensures that the zero temperature staggered moment for the Hubbard model is a monotonously decreasing function of t/U, despite the fact that the moment of the spin Hamiltonien, which depends on transverse spin fluctuations only, in an increasing function of t/U. We also comment on quantitative aspects of the t/U and 1/S expansions.