Algebraic Bethe ansatz for the supersymmetricUmodel

Abstract

We present an algebraic Bethe ansatz for the supersymmetric U model for correlated electrons on the unrestricted 4 L -dimensional electronic Hilbert space L nϭ1 C 4 ͑where L is the lattice length͒. The supersymmetry algebra of the model is the Lie superalgebra gl͑2͉1͒ and contains one symmetry-preserving free real parameter which is the Hubbard interaction parameter U. The parameter U arises from the one-parameter family of inequivalent typical four-dimensional irreps of gl͑2͉1͒. Eigenstates of the model are determined by the algebraic Bethe ansatz on a one-dimensional periodic lattice. ͓S0163-1829͑96͒03232-8͔

Analytic Bethe ansatz related to a one-parameter family of finite-dimensional representations of the Lie superalgebra

“…). We can find various kinds of the Bethe ansatz equations, which are related to the special cases of the BAE (3.1) in many literatures (for example, [11,15,17,37,38,39,40]; see also [6,14,16,41]). We suppose that the origin of the left hand side of the BAE (3.1) goes back to the ratio of some 'Drinfeld polynomials' P a (ζ) (1 ≤ a ≤ r + s + 1) labeled by the Young superdiagram with shape µ:…”

Integrable multiparametric quantum spin chains

“…Both models are gl(2/1) invariant and their formulation through the quantum inverse scattering method can be found in [8] and [31], respectively. The first model describes electrons with nearest-neighbor hopping and spin exchange interaction on a chain, while the second can be considered an extension of the Hubbard model with additional pair-hopping and bond-charge interaction terms.…”

Algebraic Bethe ansatz for a class of coupled asymmetric six-vertex free-fermion model

“…As far as the Hilbert space is concerned one would be tempted to compare these equations with that of the supersymmetric U model [15]. However, this demands that the continuous parameter governing the four dimensional representation of the superalgebra spl(2|1) reaches the value related to atypical representations which is not permitted in this model [16,17]. These remarks are strong evidences that the class of models solved here lies in between these two supersymmetric systems motivating subsequent investigations.…”

“…which together with the commutation rule (17) implies that the field D(λ) does not produce unwanted terms in the space of states generated by the creation fields B(λ).…”

“…In order to do that we use the commutation rules (15)(16)(17) and the property (21) to commute the diagonal operator through all the B(λ i ) fields until they hit the reference state. Their values acting on the reference state can be read out from Eq.(9).…”