Document Type
Article
Publication Date
11-1-2016
Publication Title
Computer Physics Communications
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. To illustrate this point, we show a brief performance comparison of accelerated versus unaccelerated methods across spatial dimensions.
Keywords
Harmonic trap, Quantum Monte Carlo, Ultracold gases
Volume
208
First Page
103
Last Page
108
DOI
10.1016/j.cpc.2016.08.005
ISSN
00104655
Recommended Citation
Berger, Casey E.; Drut, Joaquín E.; and Porter, William J., "Hard-Wall and Non-Uniform Lattice Monte Carlo Approaches to One-Dimensional Fermi Gases in a Harmonic Trap" (2016). Physics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/phy_facpubs/103
Comments
Peer reviewed accepted manuscript.