Document Type
Article
Publication Date
5-20-2015
Publication Title
Physical Review A - Atomic, Molecular, and Optical Physics
Abstract
We determine the ground-state energy and Tan's contact of attractively interacting few-fermion systems in a one-dimensional harmonic trap, for a range of couplings and particle numbers. Complementing those results, we show the corresponding density profiles. The calculations were performed with a lattice Monte Carlo approach based on a nonuniform discretization of space, defined via Gauss-Hermite quadrature points and weights. This particular coordinate basis is natural for systems in harmonic traps, and can be generalized to traps of other shapes. In all cases, it yields a position-dependent coupling and a corresponding nonuniform Hubbard-Stratonovich transformation. The resulting path integral is performed with hybrid Monte Carlo as a proof of principle for calculations at finite temperature and in higher dimensions. We present results for N=4,...,20 particles (although the method can be extended beyond that) to cover the range from few- to many-particle systems. This method is exact up to statistical and systematic uncertainties, which we account for - and thus also represents an ab initio calculation of this system, providing a benchmark for other methods and a prediction for ultracold-atom experiments.
Volume
91
Issue
5
DOI
10.1103/PhysRevA.91.053618
ISSN
10502947
Rights
©2015 American Physical Society
Recommended Citation
Berger, Casey E.; Anderson, E. R.; and Drut, J. E., "Energy, Contact, and Density Profiles of One-Dimensional Fermions in a Harmonic Trap via Nonuniform-Lattice Monte Carlo Calculations" (2015). Physics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/phy_facpubs/105
Comments
Archived as published.