Antiferromagnetic gap in the Hubbard model

TL;DR

This paper investigates the temperature-dependent antiferromagnetic gap in the 2D Hubbard model using a functional renormalization group approach with composite bosons, revealing insights into symmetry breaking and critical behavior.

Contribution

It introduces a novel method employing composite bosonic degrees of freedom within the functional renormalization group to study antiferromagnetic order in the Hubbard model.

Findings

The antiferromagnetic gap persists at finite temperatures.

Spontaneous symmetry breaking occurs despite the Mermin–Wagner theorem.

Critical behavior is influenced by Goldstone boson fluctuations.

Abstract

We compute the temperature dependence of the antiferromagnetic order parameter and the gap in the two dimensional Hubbard model at and close to half filling. Our approach is based on truncations of an exact functional renormalization group equation. The explicit use of composite bosonic degrees of freedom permits a direct investigation of the ordered low temperature phase. We show that the Mermin--Wagner theorem is not practically applicable for the spontaneous breaking of the continuous spin symmetry in the antiferromagnetic state. The critical behavior is dominated by the fluctuations of composite Goldstone bosons.