Quantum Monte Carlo study of effective masses in a polarized unitary Fermi gas

Ultracold gases provide an ideal platform for quantum simulations of many-body systems. Here we are interested in a particular system which has been the focus of most experimental and theoretical works on ultracold fermionic gases: the unitary Fermi gas. In this work we study with Quantum Monte Carlo simulations a two-component gas of fermionic atoms at zero temperature in the unitary regime. Specifically, we are interested in studying how the effective masses for the quasi-particles of the two components of the Fermi liquid evolve as the polarization is progressively reduced from full to lower values. A recent theoretical work, based on alternative diagrammatic methods, has indeed suggested that such effective masses should diverge at a critical polarization. To independently verify such predictions, we perform Variational Monte Carlo (VMC) calculations of the energy based on Jastrow-Slater wavefunctions after adding or subtracting a particle with a given momentum to a full Fermi sphere. In this way, we determine the quasi-particle dispersions, from which we extract the effective masses for different polarizations. The resulting effective masses turn out to be quite close to the non-interacting values, even though some evidence of an increase for the effective mass of the minority component appears close to the predicted value for the critical polarization. Preliminary results obtained for the majority component with the Fixed-node Diffusion Monte Carlo (DMC) method seem to indicate that DMC could lead to an increase of the effective masses in comparison with the VMC results. Finally, we point out further improvements of the trial wave-function and boundary conditions that would be necessary in future simulations to draw definite conclusions on the effective masses of the polarized unitary Fermi gas.