  I perform lattice Monte Carlo studies of universal four-component fermion
systems in one spatial dimension. Continuum few-body observables (i.e.,
ground-state energies and integrated contact densities) are determined for both
unpolarized and polarized systems of up to eight fermions confined to a
harmonic trap. Estimates of the continuum energies for four and five trapped
fermions show agreement with exact analytic calculations to within
approximately one percent statistical uncertainties. Continuum many-body
observables are determined for unpolarized systems of up to 88 fermions
confined to a finite box, and 56 fermions confined to a harmonic trap. Results
are reported for universal quantities such as the Bertsch parameter, defined as
the energy of the untrapped many-body system in units of the corresponding
free-gas energy, and its subleading correction at large but finite scattering
length. Two independent estimates of these quantities are obtained from
thermodynamic limit extrapolations of continuum extrapolated observables. A
third estimate of the Bertsch parameter is obtained by combining estimates of
the untrapped and trapped integrated contact densities with additional
theoretical input from a calculation based on Thomas-Fermi theory. All
estimates of the Bertsch parameter and its subleading correction are found to
be 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.
