Exact study of correlation functions for spin-1/2 Heisenberg chain

Jun Sato, Masahiro Shiroishi, Minoru Takahashi

Minoru Takahashi, Masahiro Shiroishi

N Kitanine, Jean Michel Maillet, N. A. Slavnov +1 more

Herman E. Boos, Masahiro Shiroishi, M. Takahashi

Masahiro Shiroishi, Minoru Takahashi

We review the recent progresses of the exact calculation of the correlation functions for the spin-1/2 Heisenberg XXX chain as well as the anisotropic XXZ chain. The spin-1/2 Heisenberg chain is exactly solvable by Bethe ansatz. Nevertheless the exact calculation of the correlation functions is still a very difficult problem in general. However, the recent theoretical developments have enabled us to derive the explicit analytical forms of some correlation functions in short range. For example, polynomial representations in terms of the one-dimensional integrals are obtained for the correlation functions of the XXZ chain up to four lattice sites. For the special case of the XXX chain, the correlation functions are further calculated up to five lattice sites.

N Kitanine, Jean Michel Maillet, N. A. Slavnov +1 more

We review some recent advances in the computation of exact correlation functions of the XXZ-½ Heisenberg chain. We first give a general introduction to our method which is based on the algebraic Bethe ansatz and the resolution of the quantum inverse scattering problem, leading in particular to multiple integral representations for the correlation functions. Then we describe recently obtained compact formulas for the spin-spin correlation functions of the XXZ-½ Heisenberg chain. We outline how this leads to several explicit results including the known two point functions in the limit of free fermions, the so-called emptiness formation probability at anisotropy Δ=1/2 and its large distance asymptotic behaviour in the massless phase of the model.