English

Computation of static Heisenberg-chain correlators: Control over length and temperature dependence

Strongly Correlated Electrons 2016-06-06 v3 High Energy Physics - Theory

Abstract

We communicate results on correlation functions for the spin-1/2 Heisenberg-chain in two particularly important cases: (a) for the infinite chain at arbitrary finite temperature TT, and (b) for finite chains of arbitrary length LL in the ground-state. In both cases we present explicit formulas expressing the short-range correlators in a range of up to seven lattice sites in terms of a single function ω\omega encoding the dependence of the correlators on TT (LL). These formulas allow us to obtain accurate numerical values for the correlators and derived quantities like the entanglement entropy. By calculating the low TT (large LL) asymptotics of ω\omega we show that the asymptotics of the static correlation functions at any finite distance are T2T^2 (1/L21/L^2) terms. We obtain exact and explicit formulas for the coefficients of the leading order terms for up to eight lattice sites.

Keywords

Cite

@article{arxiv.1105.4447,
  title  = {Computation of static Heisenberg-chain correlators: Control over length and temperature dependence},
  author = {Jun Sato and Britta Aufgebauer and Hermann Boos and Frank Göhmann and Andreas Klümper and Minoru Takahashi and Christian Trippe},
  journal= {arXiv preprint arXiv:1105.4447},
  year   = {2016}
}

Comments

5 pages, 3 figures, v2: text slightly shortened, typos in eqns. (16), (17) corrected, Fig. 1 replaced, v3: typo in eqn. (11) corrected