  In this paper, we investigate how much of the numerical artefacts introduced
by finite system size and choice of boundary conditions can be removed by
finite size scaling, for strongly-correlated systems with quasi-long-range
order. Starting from the exact ground-state wave functions of hardcore bosons
and spinless fermions with infinite nearest-neighbor repulsion on finite
periodic chains and finite open chains, we compute the two-point,
density-density, and pair-pair correlation functions, and fit these to various
asymptotic power laws. Comparing the finite-periodic-chain and finite-openchain
correlations with their infinite-chain counterparts, we find reasonable
agreement among them for the power-law amplitudes and exponents, but poor
agreement for the phase shifts. More importantly, for chain lengths on the
order of 100, we find our finite-open-chain calculation overestimates some
infinite-chain exponents (as did a recent density-matrix renormalization-group
(DMRG) calculation on finite smooth chains), whereas our finite-periodic-chain
calculation underestimates these exponents. We attribute this systematic
difference to the different choice of boundary conditions. Eventually, both
finite-chain exponents approach the infinite-chain limit: by a chain length of
1000 for periodic chains, and > 2000 for open chains. There is, howwever, a
misleading apparent finite size scaling convergence at shorter chain lengths,
for both our finite-chain exponents, as well as the finite-smooth-chain
exponents. Implications of this observation are discussed.
