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

Understand

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.