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I perform lattice Monte Carlo studies of universal four-component fermionsystems in one spatial dimension. Continuum few-body observables (i.e.,ground-state energies and integrated contact densities) are determined for bothunpolarized and polarized systems of up to eight fermions confined to aharmonic trap. Estimates of the continuum energies for four and five trappedfermions show agreement with exact analytic calculations to withinapproximately one percent statistical uncertainties. Continuum many-bodyobservables are determined for unpolarized systems of up to 88 fermionsconfined to a finite box, and 56 fermions confined to a harmonic trap. Resultsare reported for universal quantities such as the Bertsch parameter, defined asthe energy of the untrapped many-body system in units of the correspondingfree-gas energy, and its subleading correction at large but finite scatteringlength. Two independent estimates of these quantities are obtained fromthermodynamic limit extrapolations of continuum extrapolated observables. Athird estimate of the Bertsch parameter is obtained by combining estimates ofthe untrapped and trapped integrated contact densities with additionaltheoretical input from a calculation based on Thomas-Fermi theory. Allestimates of the Bertsch parameter and its subleading correction are found tobe consistent to within approximately one percent statistical uncertainties.Finally, the continuum restoration of virial theorems is verified for both few-and many-body systems confined to a trap.

Numerical study of unitary fermions in one spatial dimension