First Principles Prediction of the Landau Parameter for Fermi Liquids near the Unitarity Limit

Abstract

This paper explores the behavior of systems of cold fermions as they approach unitarity above the critical temperature. As we move away from unitarity, by decreasing the scattering length, the dilaton, the Goldstone boson resulting from the spontaneous breaking of Schrodinger symmetry by the Fermi sea, becomes gapped. At energies below this gap, the interaction between quasi-particles will be dominated by local interactions generated by off-shell dilaton exchange. The dilaton mass can, in turn, be related via anomaly matching, to the scattering length and contact parameter within the confines of a systematic expansion. We use this relation to predict the s-wave Landau parameter to be $f=\frac{4πa (2ε(p_F)-p_F^2/m_\star)^2 m}{3p_F^4 \tilde{C}(a)}$ where $a$ is the scattering length, $m$ the atomic mass, $m_\star$, the effective mass which can be extracted from heat capacity, and $\tilde {C}(a)$ is the dimensionless contact parameter. The range of validity of this prediction (given in eq.(21)) is determined by the value of contact parameter and Fermi velocity, which depend upon the scattering length. It is expected to be valid in a range above $k_F a \sim 1$, but the actual window will depend upon the values of aforementioned parameters. Given this result for $f$, we predict the compressibility, spin susceptibility and the quasi-particle life-time.