Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2011-05-23
Phys. Rev. Lett.106:257201, 2011
Physics
Condensed Matter
Strongly Correlated Electrons
5 pages, 3 figures, v2: text slightly shortened, typos in eqns. (16), (17) corrected, Fig. 1 replaced
Scientific paper
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 $T$, and (b) for finite chains of arbitrary length $L$ 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 $\omega$ encoding the dependence of the correlators on $T$ ($L$). These formulas allow us to obtain accurate numerical values for the correlators and derived quantities like the entanglement entropy. By calculating the low $T$ (large $L$) asymptotics of $\omega$ we show that the asymptotics of the static correlation functions at any finite distance are $T^2$ ($1/L^2$) terms. We obtain exact and explicit formulas for the coefficients of the leading order terms for up to eight lattice sites.
Aufgebauer Britta
Boos Hermann
Göhmann Frank
Klümper Andreas
Sato Jun
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