T. V. Skrypnyk, ““Twisted” rational <nobr>$r$</nobr>-matrices and the algebraic Bethe ansatz: Applications to generalized Gaudin models, Bose–Hubbard dimers, and Jaynes–Cummings–Dicke-type models”, TMF, 2016, Volume 189, Number 1,Pages <nobr>125

This article is cited in 6 papers

“Twisted” rational $r$-matrices and the algebraic Bethe ansatz: Applications to generalized Gaudin models, Bose–Hubbard dimers, and Jaynes–Cummings–Dicke-type models

T. V. Skrypnyk^ab

^a Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine
^b University of Milano-Bicocca, Milano, Italy

Abstract: We construct quantum integrable systems associated with the Lie algebra $gl(n)$ and non-skew-symmetric "shifted and twisted" rational $r$-matrices. The obtained models include Gaudin-type models with and without an external magnetic field, $n$-level $(n-1)$-mode Jaynes–Cummings–Dicke-type models in the $\Lambda$-configuration, a vector generalization of Bose–Hubbard dimers, etc. We diagonalize quantum Hamiltonians of the constructed integrable models using a nested Bethe ansatz.

Keywords: integrable system, classical $r$-matrix, algebraic Bethe ansatz.

MSC: 17B80, 81R12, 82B23

DOI: 10.4213/tmf9078