First Principle Predictions for Cold Fermionic Gases Near Criticality via Critical Boson Dominance and Anomaly Matching

Abstract

Recently the authors have developed an effective field theory formalism to systematically describe cold fermionic gases near the unitary limit. The theory has enhanced predictive power due to the fact that interactions are dominated by the exchange of a gapped critical boson whose couplings and mass are fixed by matching the dilatation anomaly between the UV and IR theories. We utilize this theory to give analytic predictions for the compressibility and magnetic susceptibility for fermions near unitarity with attractive interactions above the critical temperature $T_c$, with a well defined theoretical error. The inputs to the predictions are: the scattering length $a$, the effective mass $m^\star$ and contact parameter $\tilde C(a)$. We then compare our predictions to numerical simulations and find excellent agreement within the window of scattering lengths where the EFT is valid ($10\geq \mid \! k_F a \! \mid\geq 1$). Experimental corroboration of this theory supports critical point that can be describe by the inclusion of a scalar dilaton mode, whose action is fixed by symmetries.