Functional renormalization for spontaneous symmetry breaking in the Hubbard model

TL;DR

This paper uses the functional renormalization group to analyze spontaneous symmetry breaking in the 2D Hubbard model, revealing the interplay and mutual exclusion of antiferromagnetic and superconducting orders.

Contribution

It introduces composite boson fields to efficiently study symmetry-breaking regimes and computes the phase diagram and order parameter temperature dependence.

Findings

Antiferromagnetic and superconducting orders tend to exclude each other.

The phase diagram shows regions of dominant magnetic or superconducting order.

Order parameters decrease with temperature below the critical point.

Abstract

The phases with spontaneously broken symmetries corresponding to antiferromagnetic and d-wave superconducting order in the two-dimensional t-t'-Hubbard model are investigated by means of the functional renormalization group. The introduction of composite boson fields in the magnetic, charge density and superconducting channels allows an efficient parameterization of the four-fermion vertex and the study of regimes where either the antiferromagnetic or superconducting order parameter, or both, are nonzero. We compute the phase diagram and the temperature dependence of the order parameter below the critical temperature, where antiferromagnetic and superconductiving order show a tendency of mutual exclusion.