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

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.

11 pages, 8 figures

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• Pairing and the spin susceptibility of the polarized unitary Fermi gas in the normal phase
• Beyond-mean-field description of a trapped unitary Fermi gas with mass and population imbalance
• Pairing patterns in polarized unitary Fermi gases above the superfluid transition
• ${\mathbb{Z}}_4$-symmetric perturbations to the XY model from functional renormalization
• Stability of the Fulde-Ferrell-Larkin-Ovchinnikov states in anisotropic systems and critical behavior at thermal $m$-axial Lifshitz points
• Unconventional pairing in few-fermion systems at finite temperature
• Quantum Lifshitz points in an altermagnetic metal
• Effective binding potential from Casimir interactions: the case of the Bose gas
• Spin-orbit coupled mean-field Bose gas at finite temperature
• A lattice pairing-field approach to ultracold Fermi gases