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

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arxiv 1105.4447 v3 pith:DH4S5L5F submitted 2011-05-23 cond-mat.str-el hep-th

classification cond-mat.str-elhep-th
keywords correlatorsfiniteformulastermsarbitraryasymptoticscasescorrelation
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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 $T$, 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.

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  1. Current operators in Bethe Ansatz and Generalized Hydrodynamics: An exact quantum/classical correspondence

    cond-mat.stat-mech 2019-08 conditional novelty 8.0 of 10

    An exact finite-volume formula for current expectation values in Bethe ansatz models is derived, proving the GHD current conjecture for interacting lattice systems.

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