One-Parameter Matrix Representation of spl(2,1) Superalgebra

Yongqing Chen, Zheng-De Deng

Yongqing Chen

Yao-Zhong Zhang, Jason L. Werry

Abstract We present a general formula for constructing R-matrices with non-additive spectral parameters associated with a type-I quantum superalgebra. The spectral parameters originate from two one-parameter families of inequivalent finite-dimensional irreducible representations of the quantum superalgebra upon which the R-matrix acts. Applying to the quantum superalgebra Uq(gl(2|1)), we obtain the explicit expression for the Uq(gl(2|1))− invariant R-matrix which is of non-difference form in spectral parameters. Using this R­ matrix we derive a new two-parameter integrable model of strongly correlated electrons with pure imaginary pair hopping terms.

Jeongwan Haah

Arthur Hutsalyuk, Andrii Nikolaevich Liashyk, Stanislav Zdislavovich Pakuliak +2 more

We study integrable models solvable by the nested algebraic Bethe ansatz and described by gl ( 2 | 1 ) or gl ( 1 | 2 ) superalgebras. We obtain explicit determinant representations for form factors of the monodromy matrix entries. We show that all form factors are related to each other at special limits of the Bethe parameters. Our results allow one to obtain determinant formulas for form factors of local operators in the supersymmetric t – J model.

Vishnu K. Agrawala