Temperature correlation functions in the XX0 Heisenberg chain. I

Dynamical correlation functions of the spin- chain

“…In Appendix B we explain how one can deduce from this expression the result obtained in [29] in the case of free fermions.…”

“…These lemmas are used in Sections 4 and 5. In Appendix B we compare the representation (6.16) for the dynamical σ z correlation function at ∆ = 0 with the one obtained in [29] in the case of free fermions.…”

“…[10,11,12,13,14,15,16,17,18,19,20,21]). As for the dynamical correlation functions, up to now, the only known exact results concern the case of free fermions ∆ = 0 [22,23,24,25,26,27,28,29].…”

Spin–spin correlation functions of the XXZ- Heisenberg chain in a magnetic field

“…Finally, to evaluate the expectation value (3.1), it remains to compute scalar products of the type 10) where N j=1 B(λ j )|0 is an eigenstate of the transfer matrix, while the parameters {µ j } 1≤j≤N are arbitrary. The result for (3.10) is given by [19,22] (see [14] for another proof):…”

“…Although the method to compute eigenstates and energy levels goes back to H. Bethe in 1931 [1,2,3,4], the knowledge of its spin correlation functions has been for a long time restricted to the free fermion point ∆ = 0, a case for which nevertheless tremendous works have been necessary to obtain full answers [5,6,7,8,9,10].…”