Integrable spin-boson interaction in the Tavis-Cummings model from a generic boundary twist

2003/09/30 by Luigi Amico, Kazuhiro Hikami · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Quantum Information and Cryptography #Quantum and electron transport phenomena #cond-mat.str-el #hep-th #math-ph #math.MP #nlin.SI #physics.atom-ph

paper · pdf · doi:10.1140/epjb/e2005-00068-8

published as Eur.Phys.J. B43 (2005) 387 · 6 pages, revtex; 1 figure. To be published in EPJB

arxiv created 2004/12/14 · openalex publication_date 2005/02/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct models describing interaction between a spin s and a single bosonic mode using a quantum inverse scattering procedure. The boundary conditions are generically twisted by generic matrices with both diagonal and off-diagonal entries. The exact solution is obtained by mapping the transfer matrix of the spin-boson system to an auxiliary problem of a spin-j coupled to the spin-s with general twist of the boundary condition. The corresponding auxiliary transfer matrix is diagonalized by a variation of the method of Q-matrices of Baxter. The exact solution of our problem is obtained applying certain large-j limit to su(2)_j, transforming it into the bosonic algebra.

Citations

• Quantum Inverse Scattering Method and Correlation Functions
• Algebraic Approach in Unifying Quantum Integrable Models
• Lie Groups, Lie Algebras, and Some of Their Applications
• Laser cooling of trapped ions in a standing wave
• Boundary conditions for integrable quantum systems

Cited by

• Separation of variables for integrable spin–boson models
• Anisotropic Rabi model