×

Quantum KZ equation with \(| q| =1\) and correlation functions of the \(XXZ\) model in the gapless regime. (English) Zbl 0896.35114

Summary: An integral solution to the quantum Knizhnik-Zamolodchikov equation with \(| q| =1\) is presented. Upon specialization, it leads to a conjectural formula for correlation functions of the \(XXZ\) model in the gapless regime. The validity of this conjecture is verified in special cases, including the nearest-neighbour correlator with an arbitrary coupling constant and general correlators in the \(XXX\) and \(XY\) limits.

MSC:

35Q40 PDEs in connection with quantum mechanics
82B23 Exactly solvable models; Bethe ansatz
35C05 Solutions to PDEs in closed form
32G34 Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation)
PDFBibTeX XMLCite
Full Text: DOI arXiv