Generalizations of the Supersymmetric t-J Model

Holger Frahm

Lu Huai-Xin, Wang Xiao-Qin, Fan Hong-Yi

For the generalized Jaynes-Cummings model Hamiltonian which can describe two collectively radiation atoms, we find its supersymmetric structure. Based on supersymmetric quantum mechanics theory, we introduce a supersymmetric unitary transformation, in which the supersymmetric unitary transformation operator can be constructed by supersymmetric generators of the super-Lie algebra, to diagonalize the Hamiltonian. On doing so, its eigenvalue and eigenstates are obtained.

J. Exeter, Sarben Sarkar

Sarben Sarkar

Heng Fan, Miki Wadati, Xiaoman Wang

We study the generalized supersymmetric $t\ensuremath{-}J$ model with boundaries in three different gradings: fermionic, fermionic, bosonic (FFB), bosonic, fermionic, fermionic (BFF), and fermionic, bosonic, fermionic (FBF). Starting from the trigonometric R matrix, and in the framework of the graded quantum inverse scattering method, we solve the eigenvalue problems for the supersymmetric $t\ensuremath{-}J$ model. Detailed calculations are presented to obtain the eigenvalues and Bethe ansatz equations of the supersymmetric $t\ensuremath{-}J$ model with boundaries in three different backgrounds.

Hong-Yi Fan, Liang‐shi Li

We introduce supersymmetric unitary operators to directly diagonalize some generalized Jaynes–Cummings (J–C) Hamiltonians; which more deeply shows that supersymmetry is a natural language to depict the J–C model.