Toward precision Fermi liquid theory in two dimensions

TL;DR

This paper advances the understanding of two-dimensional Fermi liquids by calculating higher-order universal corrections, resolving discrepancies with simulations, and analyzing superfluid gaps and nonuniversal effects.

Contribution

It provides the first calculation of universal energy corrections to third order in interaction strength for 2D Fermi gases, improving agreement with Monte Carlo results.

Findings

Universal corrections to energy density match Monte Carlo simulations at third order.

Next-to-leading order superfluid gap is derived.

Nonuniversal effects from effective range, p-wave, and three-body forces are quantified.

Abstract

The ultra-cold and weakly-coupled Fermi gas in two spatial dimensions is studied in an effective field theory framework. It has long been observed that universal corrections to the energy density to two orders in the interaction strength do not agree with Monte Carlo simulations in the weak-coupling regime. Here, universal corrections to three orders in the interaction strength are obtained for the first time, and are shown to provide agreement between theory and simulation. Special consideration is given to the scale ambiguity associated with the non-trivial renormalization of the singular contact interactions. The isotropic superfluid gap is obtained to next-to-leading order, and nonuniversal contributions to the energy density due to effective range effects, p-wave interactions and three-body forces are computed. Results are compared with precise Monte Carlo simulations of the energy density and the contact in the weakly-coupled attractive and repulsive Fermi liquid regimes. In addition, the known all-orders sum of ladder and ring diagrams is compared with Monte Carlo simulations at weak coupling and beyond.