Abstract The boundary algebraic Bethe Ansatz for a supersymmetric nineteen vertex-model constructed from a three-dimensional representation of the twisted quantum affine Lie superalgebra U q [ o s p ( 2 | 2 ) ( 2 ) ] ≃ U q [ C ( 2 ) ( 2 ) ] is presented. The eigenvalues and eigenvectors of Sklyanin’s transfer matrix, with diagonal reflection K -matrices, are calculated and the corresponding Bethe Ansatz equations are obtained. A numerical analysis for a small-length chain is also presented.

arXiv:1705.08953Journal of Statistical Mechanics Theory and ExperimentSep 1, 20171 citation

Fusion approach for quantum integrable system associated with the $\mathfrak{gl}(1|1)$ Lie superalgebra

Xiaotian Xu, Wen, Wuxiao, Tao Yang +2 more

arXiv:2510.27312Oct 31, 20250 citations

arXiv:nlin/0406003 · Nuclear Physics B

R-matrices and spectrum of vertex models based on superalgebras

W. Galléas, Marcio Jose Martins

Published Aug 31, 2004• 40 citations

arXiv HTML PDF

DOI: 10.1016/j.nuclphysb.2004.08.002

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Fusion approach for quantum integrable system associated with the $\mathfrak{gl}(1|1)$ Lie superalgebraFusion approach for quantum integrable system associated with the $\mathfrak{gl}(1|1)$ Lie superalgebra

Xiaotian Xu, Wen, Wuxiao, Tao Yang +2 more

In this work we obtain the exact solution of quantum integrable system associated with the Lie superalgebra $\mathfrak{gl}(1|1)$ , both for periodic and for generic open boundary conditions. By means of the fusion technique we derive a closed set of operator identities among the fused transfer matrices. These identities allow us to determine the complete energy spectrum and the corresponding Bethe ansatz equations of the model. Our approach furnishes a systematic framework for studying the spectra of quantum integrable models based on Lie superalgebras, in particular when the $U(1)$ symmetry is broken. The derivation of the Bethe states from the exact spectrum is also addressed.In this work we obtain the exact solution of quantum integrable system associated with the Lie superalgebra $\mathfrak{gl}(1|1)$, both for periodic and for generic open boundary conditions. By means of the fusion technique we derive a closed set of operator identities among the fused transfer matrices. These identities allow us to determine the complete energy spectrum and the corresponding Bethe ansatz equations of the model. Our approach furnishes a systematic framework for studying the spectra of quantum integrable models based on Lie superalgebras, in particular when the $U(1)$ symmetry is broken. The derivation of the Bethe states from the exact spectrum is also addressed.

arXiv:2510.27312Oct 31, 20250 citations

Fusion approach for quantum integrable system associated with the

\mathfrak{gl}(1|1)

Lie superalgebra

In this work we obtain the exact solution of quantum integrable system associated with the Lie superalgebra

\mathfrak{gl}(1|1)

, both for periodic and for generic open boundary conditions. By means of the fusion technique we derive a closed set of operator identities among the fused transfer matrices. These identities allow us to determine the complete energy spectrum and the corresponding Bethe ansatz equations of the model. Our approach furnishes a systematic framework for studying the spectra of quantum integrable models based on Lie superalgebras, in particular when the

U(1)

symmetry is broken. The derivation of the Bethe states from the exact spectrum is also addressed.