New results in the XXZ open spin chain
Pascal Baseilhac (LMPT)
TL;DR
This paper reviews a recent algebraic approach using the $q$-Onsager algebra to derive exact solutions for the spectrum and eigenstates of the XXZ open spin chain, highlighting new mathematical insights.
Contribution
It introduces a novel method based on the $q$-Onsager algebra to obtain exact spectral and eigenstate results for the XXZ open spin chain.
Findings
Complete spectrum and eigenstates expressed as rational functions
Eigenvalues correspond to roots of a characteristic polynomial
Provides insights and open problems in the algebraic approach
Abstract
In this review, I describe a recent approach based on the representation theory of the Onsager algebra which is used to derive exact results for the XXZ open spin chain. The complete spectrum and eigenstates are obtained as rational functions of a single variable which discrete values correspond to the roots of a certain characteristic polynomial. Comments and open problems are also presented.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra