Understanding finite size effects in quasi-long-range orders for exactly solvable chain models

Details Understanding finite size effects in quasi-long-range orders for exactly solvable chain models Understanding finite size effects in quasi-long-range orders for exactly solvable chain models

2010-07-14

arxiv.org/abs/1007.2257v2

Physics

Condensed Matter

Strongly Correlated Electrons

14 pages, 15 figures

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Understanding finite size effects in quasi-long-range orders for exactly solvable chain models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Understanding finite size effects in quasi-long-range orders for exactly solvable chain models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Understanding finite size effects in quasi-long-range orders for exactly solvable chain models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-120323