Two-particle self-consistent approach for broken symmetry phases

TL;DR

This paper extends the Two-Particle Self-Consistent method to broken symmetry phases in the Hubbard model, effectively capturing strong correlations and providing results that agree with Diagrammatic Monte Carlo, including insights into Higgs modes.

Contribution

It introduces a generalized TPSC approach for magnetic broken symmetry phases, incorporating sum-rule enforcement and vertex corrections for accurate description of the Hubbard model.

Findings

Excellent quantitative agreement with Diagrammatic Monte Carlo for double occupancies and magnetization.

Vertex corrections significantly influence the Higgs resonance in spin susceptibilities.

The method preserves Goldstone modes and correctly renormalizes the order parameter.

Abstract

Spontaneous symmetry breaking of interacting fermion systems constitutes a major challenge for many-body theory due to the proliferation of new independent scattering channels once absent or degenerate in the symmetric phase. One example is given by the ferro/antiferromagnetic broken symmetry phase (BSP) of the Hubbard model, where vertices in the spin-transverse and spin-longitudinal channels become independent with a consequent increase in the computational power for their calculation. We generalise the non-perturbative Two-Particle- Self-Consistent method (TPSC) to address broken SU(2) magnetic phases in the Hubbard model, offering an efficient approach that incorporates strong correlations. We show that in the BSP, the sum-rule enforcement of susceptibilities must be accompanied by a modified gap equation resulting in a renormalisation of the order parameter, vertex corrections and the preservation of the gap-less feature of the Goldstone modes. We then apply the theory to the antiferromagnetic phase of the Hubbard model in the cubic lattice at half-filling. We compare our results of double occupancies and staggered magnetisation to the ones obtained using Diagrammatic Monte Carlo showing excellent quantitative agreement. We demonstrate how vertex corrections play a central role in lowering the Higgs resonance with respect to the quasi-particle excitation gap in the spin-longitudinal susceptibility, yielding a well visible Higgs-mode.