Doping of a spin-1 chain: integrable model

An exactly soluble model describing a spin S=1 antiferromagnetic chain doped with mobile S=1/2 carriers is constructed. In its continuum limit the undoped state is described by three gapless Majorana fermions composing the SU(2) triplet. Doping adds to this a scalar charge field and a singlet Majorana fermion with different velocity. We argue that this mode survives when the Haldane gap is added.Comment: RevTeX, 6 pages, 3 figures; final version, to appear in PR

Algebraic Bethe ansatz for the gl(1∣|2) generalized model II: the three gradings

The algebraic Bethe ansatz can be performed rather abstractly for whole classes of models sharing the same $R$-matrix, the only prerequisite being the existence of an appropriate pseudo vacuum state. Here we perform the algebraic Bethe ansatz for all models with $9 \times 9$, rational, gl(1$|$2)-invariant $R$-matrix and all three possibilities of choosing the grading. Our Bethe ansatz solution applies, for instance, to the supersymmetric t-J model, the supersymmetric $U$ model and a number of interesting impurity models. It may be extended to obtain the quantum transfer matrix spectrum for this class of models. The properties of a specific model enter the Bethe ansatz solution (i.e. the expression for the transfer matrix eigenvalue and the Bethe ansatz equations) through the three pseudo vacuum eigenvalues of the diagonal elements of the monodromy matrix which in this context are called the parameters of the model.Comment: paragraph added in section 3, reference added, version to appear in J.Phys.

Finite-Size Scaling Studies of Reaction-Diffusion Systems Part III: Numerical Methods

The scaling exponent and scaling function for the 1D single species coagulation model $(A+A\rightarrow A)$ are shown to be universal, i.e. they are not influenced by the value of the coagulation rate. They are independent of the initial conditions as well. Two different numerical methods are used to compute the scaling properties: Monte Carlo simulations and extrapolations of exact finite lattice data. These methods are tested in a case where analytical results are available. It is shown that Monte Carlo simulations can be used to compute even the correction terms. To obtain reliable results from finite-size extrapolations exact numerical data for lattices up to ten sites are sufficient.Comment: 19 pages, LaTeX, 5 figures uuencoded, BONN HE-94-0

Eight state supersymmetric UU model of strongly correlated fermions

An integrable eight state supersymmtric $U$ model is proposed, which is a fermion model with correlated single-particle and pair hoppings as well as uncorrelated triple-particle hopping. It has an $gl(3|1)$ supersymmetry and contains one symmetry-preserving free parameter. The model is solved and the Bethe ansatz equations are obtained.Comment: Some cosmetic changes; to appear in Phys. Rev.

Transfer matrix eigenvalues of the anisotropic multiparametric U model

A multiparametric extension of the anisotropic U model is discussed which maintains integrability. The R-matrix solving the Yang-Baxter equation is obtained through a twisting construction applied to the underlying Uq(sl(2|1)) superalgebraic structure which introduces the additional free parameters that arise in the model. Three forms of Bethe ansatz solution for the transfer matrix eigenvalues are given which we show to be equivalent.Comment: 26 pages, no figures, LaTe

Quantum integrability and exact solution of the supersymmetric U model with boundary terms

The quantum integrability is established for the one-dimensional supersymmetric $U$ model with boundary terms by means of the quantum inverse scattering method. The boundary supersymmetric $U$ chain is solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived. This provides us with a basis for computing the finite size corrections to the low lying energies in the system.Comment: 4 pages, RevTex. Some cosmetic changes. The version to appear in Phys. Rev.

Extended integrability regime for the supersymmetric U model

An extension of the supersymmetric U model for correlated electrons is given and integrability is established by demonstrating that the model can he constructed through the quantum inverse scattering method using an R-matrix without the difference property. Some general symmetry properties of the model are discussed and from the Bethe ansatz solution an expression for the energies is presented