On the complete-spectrum characterization of quantum integrable spin chains via inhomogeneous T–Q relation. (15th October 2015)

• Record Type: Journal Article
• Authors: Cao, Junpeng; Yang, Wen-Li; Shi, Kangjie; Wang, Yupeng
• Is Part Of: Journal of physics. Volume 48:Number 44(2015)
• Publication Date: 2015-10-15
• Subjects: Bethe Ansatz -- T–Q relation -- integrable models; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/48/44/444001
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: With the XXZ spin chains as examples, we prove two theorems: (1) the functional relations derived from the off-diagonal Bethe Ansatz scheme are the sufficient and necessary conditions to characterize the complete spectrum of the corresponding transfer matrix; (2) each eigenvalue of the transfer matrix can be parameterized by a minimal inhomogeneous T – Q relation. These statements hold for both with and without inhomogeneity. The proof can be generalized to other finite-dimensional quantum integrable models.