SciPost Submission Page
Two-particle self-consistent approach for broken symmetry phases
by Lorenzo Del Re
Submission summary
| Authors (as registered SciPost users): | Lorenzo Del Re |
| Submission information | |
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| Preprint Link: | scipost_202407_00001v1 (pdf) |
| Date submitted: | 2024-07-01 10:23 |
| Submitted by: | Del Re, Lorenzo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
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. Here we generalize the formalism of the non-perturbative Two-Particle-Self-Consistent method (TPSC) to treat broken SU(2) magnetic phases of the Hubbard model, providing with a efficient yet reliable method. 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.
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