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We determine the ground-state energy and Tan's contact of attractivelyinteracting few-fermion systems in a one-dimensional harmonic trap, for a rangeof couplings and particle numbers. Complementing those results, we show thecorresponding density profiles. The calculations were performed with a newlattice Monte Carlo approach based on a non-uniform discretization of space,defined via Gauss-Hermite quadrature points and weights. This particularcoordinate basis is natural for systems in harmonic traps, and can begeneralized to traps of other shapes. In all cases, it yields aposition-dependent coupling and a corresponding non-uniformHubbard-Stratonovich transformation. The resulting path integral is performedwith hybrid Monte Carlo as a proof of principle for calculations at finitetemperature and in higher dimensions. We present results for N=4,...,20particles (although the method can be extended beyond that) to cover the rangefrom few- to many-particle systems. This method is also exact up to statisticaland systematic uncertainties, which we account for -- and thus also representsthe first ab initio calculation of this system, providing a benchmark for othermethods and a prediction for ultracold-atom experiments.

Energy, contact, and density profiles of one-dimensional fermions in a harmonic trap via non-uniform lattice Monte Carlo