“ Z2 -graded” Gaudin models and analytical Bethe ansatz

Yupeng Wang, Wen‐Li Yang, Junpeng Cao +1 more

T. Skrypnyk

We consider quantum integrable systems associated with reductive Lie algebra g l ( n ) and Cartan-invariant non-skew-symmetric classical r -matrices. We show that under certain restrictions on the form of classical r -matrices “nested” or “hierarchical” Bethe ansatz usually based on a chain of subalgebras g l ( n ) ⊃ g l ( n − 1 ) ⊃ . . . ⊃ g l ( 1 ) is generalized onto the other chains or “hierarchies” of subalgebras. We show that among the r -matrices satisfying such the restrictions there are “twisted” or Z p -graded non-skew-symmetric classical r -matrices. We consider in detail example of the generalized Gaudin models with and without external magnetic field associated with Z p -graded non-skew-symmetric classical r -matrices and find the spectrum of the corresponding Gaudin-type hamiltonians using nested Bethe ansatz scheme and a chain of subalgebras g l ( n ) ⊃ g l ( n − n 1 ) ⊃ g l ( n − n 1 − n 2 ) ⊃ g l ( n − ( n 1 + . . . + n p − 1 ) ) , where n 1 + n 2 + . . . + n p = n .

Jun-peng Cao, Bo-Yu Hou, Rui‐Hong Yue

In this paper we propose the Hamiltonians of the generalized SU q (1|2) Gaudin model corresponding to the periodic generalized t - J model. With the help of the well defined graded quantum determinant, we obtain the eigenstate and eigenvalues of the generating function and the Hamiltonians of the Gaudin model in the fermionic background in the framework of the graded quantum inverse scattering method. The Bethe ansatz equations are also obtained.

N. A. Slavnov

Jon Links

E. KOZAK, R. NIEMIEC, D. GOŁOJUCH +1 more