A simple SUSY Bose-Fermi Hamiltonian and a class of hard-core Bose-Fermi Hamiltonians with high order terms constructed by using the gl(m/n) generators are shown to be exactly solvable. Excitation energies and corresponding wavefunctions are obtained by using a simple algebraic Bethe ansatz.
It is shown that the two component Fermi or Bose many-body Hamiltonian, such as the two-orbit fermion pairing and two-site Bose-Hubbard model with arbitrary finite higher order terms can always be solved exactly by using Bethe ansatz vector construction based on the permutation of two components of bosons or fermions involved. As examples of the solution, the extended one-dimensional dimer Bose -Hubbard model with multi-body interactions and the mean-fifield plus orbit-dependent non-separable pairing model with two non-degenerate j-orbits are demonstrated with the eigenstates and the eigen-energy and the related Bethe ansatz equations. It is shown that the main feature of the solutions lies in the fact that the Bethe ansatz vectors can be expressed in terms of binomials of the boson or fermion operators times the related symmetric functions. As the consequence, two-component quantum many-body systems , such as the extended Lipkin-Meshkov-Glick model with higher-order interactions, can be solved in a similar way.
A unified algebraic approach to both the hard-core Fermi– and Bose–Hubbard models is extended to both the finite- and infinite-site with periodic condition cases. Excitation energies and the corresponding wavefunctions of both the models with nearest neighbor hopping are exactly derived by using a new and simple algebraic method. It is found that spectra of both the models are determined simply by eigenvalue problem of N × N hopping matrix, where N is the number of sites for finite system or the period of sites for infinite system.