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 unitary above the critical temperature. Symmetry arguments indicate that at unitarity the Fermi-liquid picture breaks down. 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 quasiparticles will be dominated by 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 that the quasiparticle width is given by the expression $\mathrm{\ensuremath{\Gamma}}(E,T)=\frac{8m}{9\ensuremath{\pi}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\mathcal{C}}}^{2}}(\sqrt{\frac{m}{{m}^{★}}}\frac{a{\ensuremath{\mu}}_{F}^{2}}{4\ensuremath{\hbar}{E}_{F}^{2}}{)}^{2}({E}^{2}+{\ensuremath{\pi}}^{2}{k}_{B}^{2}{T}^{2})$ where $a$ is the the scattering length, ${m}_{★}$ is the effective mass, and $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\mathcal{C}}$ is the dimensionless contact parameter. This prediction is valid for ${(\frac{{E}_{F}}{E})}^{2}\ensuremath{\gg}a{k}_{f}\ensuremath{\gg}1$.