Low energy singularities in the ground state of fermionic superfluids

TL;DR

This paper investigates how order parameter fluctuations affect the ground state of fermionic superfluids, revealing singularities and their interplay through renormalization group analysis, with implications for low-energy excitations and the fermionic gap.

Contribution

It derives a minimal set of one-loop RG equations capturing the coupled singularities in fermionic superfluids, ensuring symmetry preservation and providing analytical and numerical insights.

Findings

Goldstone mode cancellations are maintained in the flow.

Flow equations describe low-energy correlations and their impact on the fermionic gap.

Numerical solutions for the 2D Hubbard model illustrate the theoretical framework.

Abstract

We analyze the effects of order parameter fluctuations on the ground state of fully gapped charge-neutral fermionic superfluids. The Goldstone mode associated with the spontaneously broken symmetry leads to a problem of coupled singularities in $d \leq 3$ dimensions. We derive a minimal set of one-loop renormalization group equations which fully captures the interplay of the singularities. The flow equations are based on a symmetry conserving truncation of a scale dependent effective action. We compute the low energy behavior of longitudinal, transverse and mixed order parameter correlations, and their impact on the fermionic gap. We demonstrate analytically that cancellations protecting the Goldstone mode are respected by the flow, and we present a numerical solution of the flow equations for the two-dimensional attractive Hubbard model.