From quantum Bäcklund transforms to topological quantum field theory. (2nd February 2016)

• Record Type: Journal Article
• Authors: Korff, Christian
• Is Part Of: Journal of physics. Volume 49:Number 10(2016)
• Publication Date: 2016-02-02
• Subjects: exactly solvable lattice models -- Bäcklund transform -- topological quantum field theory -- Baxter's Q-operator; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/49/10/104001
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We derive the quantum analogue of a Bäcklund transformation for the quantized Ablowitz–Ladik chain, a space discretization of the nonlinear Schrödinger equation. The quantization of the Ablowitz–Ladik chain leads to the q -boson model. Using a previous construction of Baxter's Q -operator for this model by the author, a set of functional relations is obtained which matches the relations of a one-variable classical Bäcklund transform to all orders in . We construct also a second Q -operator and show that it is closely related to the inverse of the first. The multi-Bäcklund transforms generated from the Q -operator define the fusion matrices of a 2D TQFT and we derive a linear system for the solution to the quantum Bäcklund relations in terms of the TQFT fusion coefficients.