Quantum Lifshitz points and fluctuation-induced first-order phase transitions in imbalanced Fermi mixtures

TL;DR

This paper investigates the nature of phase transitions in imbalanced Fermi mixtures, revealing conditions for a quantum Lifshitz point and showing how damping effects can induce a weakly first-order transition.

Contribution

It demonstrates the possibility of realizing a quantum Lifshitz point in Fermi mixtures and analyzes how damping influences the order of the phase transition.

Findings

Gradient term can be tuned to zero at T→0, enabling a quantum Lifshitz point.

Landau damping affects the order-parameter field near the transition, potentially inducing a first-order transition.

Renormalization-group analysis shows damping destabilizes the second-order transition, suggesting a weakly first-order transition.

Abstract

We perform a detailed analysis of the phase transition between the uniform superfluid and normal phases in spin- and mass-imbalanced Fermi mixtures. At mean-field level we demonstrate that at temperature $T\to 0$ the gradient term in the effective action can be tuned to zero for experimentally relevant sets of parameters, thus providing an avenue to realize a quantum Lifshitz point. We subsequently analyze damping processes affecting the order-parameter field across the phase transition. We show that, in the low energy limit, Landau damping occurs only in the symmetry-broken phase and affects exclusively the longitudinal component of the order-parameter field. It is however unavoidably present in the immediate vicinity of the phase transition at temperature $T=0$. We subsequently perform a renormalization-group analysis of the system in a situation, where, at mean-field level, the quantum phase transition is second order (and not multicritical). We find that, at $T$ sufficiently low, including the Landau damping term in a form derived from the microscopic action destabilizes the renormalization group flow towards the Wilson-Fisher fixed point. This signals a possible tendency to drive the transition weakly first-order by the coupling between the order-parameter fluctuations and fermionic excitations effectively captured by the Landau damping contribution to the order-parameter action.