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 $f=\frac{4\pi a(2\epsilon (p_F)-p_F^2/m_{\star }{)}^{2}m}{3p_F^4\tilde{C}(a)}$ 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.

arXiv commentThis replacement contains an improved discussion of the range of validity of the EFT and includes a prediction for the spin susceptibility of the Fermi gas. It also fixes an error in the prediction for the Landau parameter and the compressibility in the earlier version

References in corpus (15)

• Renormalization Group Approach to Interacting Fermions
• Universality in Few-body Systems with Large Scattering Length
• Bose-Einstein condensation of atoms in a uniform potential
• Energetics of a strongly correlated Fermi gas
• Verification of universal relations in a strongly interacting Fermi gas
• Homogeneous Atomic Fermi Gases
• Quantum Gases in Optical Boxes
• Two-Dimensional Homogeneous Fermi Gases
• Excitation Spectrum and Superfluid Gap of an Ultracold Fermi Gas
• Criterion for stability of Goldstone Modes and Fermi Liquid behavior in a metal with broken symmetry
• Ground-state thermodynamic quantities of homogeneous spin-$1/2$ fermions from the BCS region to the unitarity limit
• Measuring the Hydrodynamic Linear Response of a Unitary Fermi Gas
• Spontaneously broken boosts and the Goldstone continuum
• Symmetry Obstruction to Fermi Liquid Behavior in the Unitary Limit
• Symmetry Realization via a Dynamical Inverse Higgs Mechanism

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