Non-additive fusion, Hubbard models and non-locality

In the framework of quantum groups and additive R-matrices, the fusion procedure allows to construct higher-dimensional solutions of the Yang-Baxter equation. These solutions lead to integrable one-dimensional spin-chain Hamiltonians. Here fusion is shown to generalize naturally to non-additive R-matrices, which therefore do not have a quantum group symmetry. This method is then applied to the generalized Hubbard models. Although the resulting integrable models are not as simple as the starting ones, the general structure is that of two spin-(s times s') sl(2) models coupled at the free-fermion point. An important issue is the probable lack of regular points which give local Hamiltonians. This problem is related to the existence of second order zeroes in the unitarity equation, and arises for the XX models of higher spins, the building blocks of the Hubbard models. A possible connection between some Lax operators L and R-matrices is noted.Comment: 14 pages, Latex. A remark added in section 2, four typos correcte

New Integrable Models from Fusion

Integrable multistate or multiflavor/color models were recently introduced. They are generalizations of models corresponding to the defining representations of the U_q(sl(m)) quantum algebras. Here I show that a similar generalization is possible for all higher dimensional representations. The R-matrices and the Hamiltonians of these models are constructed by fusion. The sl(2) case is treated in some detail and the spin-0 and spin-1 matrices are obtained in explicit forms. This provides in particular a generalization of the Fateev-Zamolodchikov Hamiltonian.Comment: 11 pages, Latex. v2: statement concerning symmetries qualified, 3 minor misprints corrected. J. Phys. A (1999) in pres

Including a phase in the Bethe equations of the Hubbard model

We compute the Bethe equations of generalized Hubbard models, and study their thermodynamical limit. We argue how they can be connected to the ones found in the context of AdS/CFT correspondence, in particular with the so-called dressing phase problem. We also show how the models can be interpreted, in condensed matter physics, as integrable multi-leg Hubbard models.Comment: 30 page

Thermodynamics of an integrable model for electrons with correlated hopping

A new supersymmetric model for electrons with generalized hopping terms and Hubbard interaction on a one-dimensional lattice is solved by means of the Bethe Ansatz. We investigate the phase diagram of this model by studying the ground state and excitations of the model as a function of the interaction parameter, electronic density and magnetization. Using arguments from conformal field theory we can study the critical exponents describing the asymptotic behaviour of correlation functions at long distances.Comment: 24 pp., latex+epsf, figures include

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.

Uqosp(2,2)U_q osp(2,2) Lattice Models

In this paper I construct lattice models with an underlying $U_q osp(2,2)$ superalgebra symmetry. I find new solutions to the graded Yang-Baxter equation. These {\it trigonometric} $R$-matrices depend on {\it three} continuous parameters, the spectral parameter, the deformation parameter $q$ and the $U(1)$ parameter, $b$, of the superalgebra. It must be emphasized that the parameter $q$ is generic and the parameter $b$ does not correspond to the `nilpotency' parameter of \cite{gs}. The rational limits are given; they also depend on the $U(1)$ parameter and this dependence cannot be rescaled away. I give the Bethe ansatz solution of the lattice models built from some of these $R$-matrices, while for other matrices, due to the particular nature of the representation theory of $osp(2,2)$, I conjecture the result. The parameter $b$ appears as a continuous generalized spin. Finally I briefly discuss the problem of finding the ground state of these models.Comment: 19 pages, plain LaTeX, no figures. Minor changes (version accepted for publication

An Intersecting Loop Model as a Solvable Super Spin Chain

In this paper we investigate an integrable loop model and its connection with a supersymmetric spin chain. The Bethe Ansatz solution allows us to study some properties of the ground state. When the loop fugacity $q$ lies in the physical regime, we conjecture that the central charge is $c=q-1$ for $q$ integer $< 2$. Low-lying excitations are examined, supporting a superdiffusive behavior for $q=1$. We argue that these systems are interesting examples of integrable lattice models realizing $c \leq 0$ conformal field theories.Comment: latex file, 7 page

Super-Hubbard models and applications

We construct XX- and Hubbard- like models based on unitary superalgebras gl(N|M) generalising Shastry's and Maassarani's approach of the algebraic case. We introduce the R-matrix of the gl(N|M) XX model and that of the Hubbard model defined by coupling two independent XX models. In both cases, we show that the R-matrices satisfy the Yang--Baxter equation, we derive the corresponding local Hamiltonian in the transfer matrix formalism and we determine the symmetry of the Hamiltonian. Explicit examples are worked out. In the cases of the gl(1|2) and gl(2|2) Hubbard models, a perturbative calculation at two loops a la Klein and Seitz is performed.Comment: 26 page

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