Correlation functions of the XXZ model for Δ < − 1

Abstract

Abstract.A new approach to the correlation functions is presented for the XXZ model in the anti-ferroelectric regime. The method is based on the recent realization of the quantum affine symmetry using vertex operators. With the aid of a boson representation for the latter, an integral formula is found for correlation functions of arbitrary local operators. As a special case it reproduces the spontaneous staggered polarization obtained earlier by Baxter.

Correlation function of the spin- XXX antiferromagnet

“…It was invented recently by the RIMS group [14]. In that paper correlation functions in the XXZ model were considered.…”

Dynamical correlation functions of the spin- chain

“…Different ways to study the time-independent correlation functions of this model were proposed in the series of works (see e.g. [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

“…However, at zero temperature and for zero magnetic field, multiple integral representations of elementary blocks of the correlation functions (see definition below) have been obtained from the q-vertex operator approach (inspired from the corner transfer matrix technique) in the massive regime ∆ > 1 in 1992 [11], and conjectured in 1996 [12] for the massless regime −1 < ∆ ≤ 1 (see also [13]). A proof of these results together with their extension to non-zero magnetic field has been obtained in 1999 [14,15] for both regimes using algebraic Bethe ansatz [16,17] and the actual resolution of the so-called quantum inverse scattering problem [14,18].…”