Harmonically-trapped Fermions in Three Dimensions: A Hard-wall Approach

Casey Berger, University of North Carolina, Chapel Hill

Ultracold atoms are among the most malleable systems that can be studied experimentally. Dimensionality, polarization, temperature and coupling strength can be tuned essentially at will. For this reason, atomic systems continue to attract attention from several areas in physics. The most interesting regimes, where phase transitions occur, appear when interactions dominate. Those regimes cannot be treated analytically and must therefore be treated computationally. In this work, we investigate the ground state energy of N spin-1/2 fermions in a harmonic trapping potential in the strong coupling regime known as the unitary limit. The fermions are placed in a uniform spatial lattice with hard-wall boundary conditions and the hybrid Monte Carlo (HMC) method is implemented. In previous work, the system was placed in a Gauss-Hermite lattice, the natural basis for a harmonic trapping potential, but the new approach allows for acceleration of the computation using fast Fourier acceleration (implemented via FFTW). The non-accelerated algorithm scales as V^2, while the accelerated version scales as V log V, where V is the spatial volume of the system (in any dimension). We reproduce our previous results for the ground state energy and contact in one dimension and calculate the energy and contact at unitarity in three dimensions. This work paves the way to more computationally intensive calculations, such as finite-temperature, multiple flavors and rotating trapping potentials.

Abstract Author(s): C.E. Berger, W.J. Porter, J.E. Drut