# Understanding finite size effects in quasi-long-range orders for exactly solvable chain models - Condensed Matter > Strongly Correlated Electrons

Understanding finite size effects in quasi-long-range orders for exactly solvable chain models - Condensed Matter > Strongly Correlated Electrons - Download this document for free, or read online. Document in PDF available to download.

Abstract: In this paper, we investigate how much of the numerical artefacts introducedby finite system size and choice of boundary conditions can be removed byfinite size scaling, for strongly-correlated systems with quasi-long-rangeorder. Starting from the exact ground-state wave functions of hardcore bosonsand spinless fermions with infinite nearest-neighbor repulsion on finiteperiodic chains and finite open chains, we compute the two-point,density-density, and pair-pair correlation functions, and fit these to variousasymptotic power laws. Comparing the finite-periodic-chain and finite-openchaincorrelations with their infinite-chain counterparts, we find reasonableagreement among them for the power-law amplitudes and exponents, but pooragreement for the phase shifts. More importantly, for chain lengths on theorder of 100, we find our finite-open-chain calculation overestimates someinfinite-chain exponents as did a recent density-matrix renormalization-groupDMRG calculation on finite smooth chains, whereas our finite-periodic-chaincalculation underestimates these exponents. We attribute this systematicdifference to the different choice of boundary conditions. Eventually, bothfinite-chain exponents approach the infinite-chain limit: by a chain length of1000 for periodic chains, and > 2000 for open chains. There is, howwever, amisleading apparent finite size scaling convergence at shorter chain lengths,for both our finite-chain exponents, as well as the finite-smooth-chainexponents. Implications of this observation are discussed.

Author: ** Sisi Tan, Siew Ann Cheong**

Source: https://arxiv.org/