Two-parameter extended Hubbard Hamiltonian with supersymmetry

Fabian H.L. Eβler

Ronaldo Silva Thibes, E. F. Batista, Gabriel D. Barbosa

We review supersymmetry (SUSY) in nonrelativistic quantum mechanics emphasizing algebraic aspects.We discuss the Hamiltonian subgroup implementing supersymmetry as well as the corresponding algebra of the SUSY generators.In the SUSYQM framework, the two distinct partner potentials are connected by a superpotential satisfying a Riccati differential equation.A full Hamiltonian operator in an extended Hilbert space is defined in order to render the supersymmetry manifest.As a result, the eigenfunctions of the original potentials are connected by generalized ladder operators.We provide an explicit realization of the abstract supersymmetry group for SUSYQM depending on one real and two Grassmann parameters.

Kareljan Schoutens

Fabian H. L. Eßler, Holger Frahm, Frank Göhmann +2 more

Katrina Hibberd, M. D. Gould, Jon Links

We present an algebraic Bethe ansatz for the anisotropic supersymmetric U model for correlated electrons on the unrestricted -dimensional electronic Hilbert space (where L is the lattice length). The supersymmetry algebra of the local Hamiltonian is the quantum superalgebra and the model contains two symmetry-preserving free real parameters; the quantization parameter q and the Hubbard interaction parameter U. The parameter U arises from the one-parameter family of inequivalent typical four-dimensional irreps of . Eigenstates of the model are determined by the algebraic Bethe ansatz on a one-dimensional periodic lattice.

Fabian H. L. Eßler, V. E. Korepin