Hard-Wall and Non-Uniform Lattice Monte Carlo Approaches to One-Dimensional Fermi Gases in a Harmonic Trap

Abstract

We present in detail two variants of the lattice Monte Carlo method aimed at tackling systems in external trapping potentials: a uniform-lattice approach with hard-wall boundary conditions, and a non-uniform Gauss-Hermite lattice approach. Using those two methods, we compute the ground-state energy and spatial density profile for systems of N=4 - 8 harmonically trapped fermions in one dimension. From the favorable comparison of both energies and density profiles (particularly in regions of low density), we conclude that the trapping potential is properly resolved by the hard-wall basis. Our work paves the way to higher dimensions and finite temperature analyses, as calculations with the hard-wall basis can be accelerated via fast Fourier transforms, the cost of unaccelerated methods is otherwise prohibitive due to the unfavorable scaling with system size.

13 pages, 3 figures

References in corpus (8)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Phase diagram of a strongly interacting polarized Fermi gas in one dimension
• The ground state energy at unitarity
• Pairing in a system of a few attractive fermions in a harmonic trap
• Pairing of few Fermi atoms in one dimension
• Successes and failures of Bethe Ansatz Density Functional Theory
• Energy, contact, and density profiles of one-dimensional fermions in a harmonic trap via non-uniform lattice Monte Carlo

Cited by in corpus (5)

• Surmounting the sign problem in non-relativistic calculations: a case study with mass-imbalanced fermions
• Few strongly interacting ultracold fermions in one-dimensional traps of different shapes
• Evolution from few- to many-body physics in one-dimensional Fermi systems: One- and two-body density matrices, and particle-partition entanglement
• Ground-state energy, density profiles, and momentum distribution of attractively interacting 1D Fermi gases with hard-wall boundaries: a Monte Carlo study
• Thermodynamics of rotating quantum matter in the virial expansion