The Unitary Fermi Gas: From Monte Carlo to Density Functionals

TL;DR

This paper explores the universal physics of the unitary Fermi gas through Monte Carlo simulations, density functional theory, and time-dependent methods, providing new computational tools and insights into its quantum properties.

Contribution

It introduces a first-principles Monte Carlo approach, develops a density functional theory fit, and extends to time-dependent dynamics for the unitary Fermi gas.

Findings

Accurate thermodynamic properties from Monte Carlo simulations.

Effective density functionals for superfluid and asymmetric systems.

Time-dependent DFT captures quantum dynamics and phase transitions.

Abstract

In this chapter, we describe three related studies of the universal physics of two-component unitary Fermi gases with resonant short-ranged interactions. First we discuss an ab initio auxiliary field quantum Monte Carlo technique for calculating thermodynamic properties of the unitary gas from first principles. We then describe in detail a Density Functional Theory (DFT) fit to these thermodynamic properties: the Superfluid Local Density Approximation (SLDA) and its Asymmetric (ASLDA) generalization. We present several applications, including vortex structure, trapped systems, and a supersolid Larkin-Ovchinnikov (FFLO/LOFF) state. Finally, we discuss the time-dependent extension to the density functional (TDDFT) which can describe quantum dynamics in these systems, including non-adiabatic evolution, superfluid to normal transitions and other modes not accessible in traditional frameworks such as a Landau-Ginzburg, Gross-Pitaevskii, or quantum hydrodynamics.