76 research outputs found
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
Matrix difference equations for the supersymmetric Lie algebra sl(2,1) and the `off-shell' Bethe ansatz
Based on the rational R-matrix of the supersymmetric sl(2,1) matrix
difference equations are solved by means of a generalization of the nested
algebraic Bethe ansatz. These solutions are shown to be of highest-weight with
respect to the underlying graded Lie algebra structure.Comment: 10 pages, LaTex, references and acknowledgements added, spl(2,1) now
called sl(2,1
Algebraic Bethe ansatz for the gl(12) generalized model II: the three gradings
The algebraic Bethe ansatz can be performed rather abstractly for whole
classes of models sharing the same -matrix, the only prerequisite being the
existence of an appropriate pseudo vacuum state. Here we perform the algebraic
Bethe ansatz for all models with , rational, gl(12)-invariant
-matrix and all three possibilities of choosing the grading. Our Bethe
ansatz solution applies, for instance, to the supersymmetric t-J model, the
supersymmetric 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.
On the solution of a supersymmetric model of correlated electrons
We consider the exact solution of a model of correlated electrons based on
the superalgebra . The corresponding Bethe ansatz equations have an
interesting form. We derive an expression for the ground state energy at half
filling. We also present the eigenvalue of the transfer matrix commuting with
the Hamiltonian.Comment: Palin latex , 8 page
Lattice Models
In this paper I construct lattice models with an underlying
superalgebra symmetry. I find new solutions to the graded Yang-Baxter equation.
These {\it trigonometric} -matrices depend on {\it three} continuous
parameters, the spectral parameter, the deformation parameter and the
parameter, , of the superalgebra. It must be emphasized that the
parameter is generic and the parameter does not correspond to the
`nilpotency' parameter of \cite{gs}. The rational limits are given; they also
depend on the parameter and this dependence cannot be rescaled away. I
give the Bethe ansatz solution of the lattice models built from some of these
-matrices, while for other matrices, due to the particular nature of the
representation theory of , I conjecture the result. The parameter
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 lies in the physical
regime, we conjecture that the central charge is for integer .
Low-lying excitations are examined, supporting a superdiffusive behavior for
. We argue that these systems are interesting examples of integrable
lattice models realizing conformal field theories.Comment: latex file, 7 page
Non-chiral current algebras for deformed supergroup WZW models
We study deformed WZW models on supergroups with vanishing Killing form. The
deformation is generated by the isotropic current-current perturbation which is
exactly marginal under these assumptions. It breaks half of the global
isometries of the original supergroup. The current corresponding to the
remaining symmetry is conserved but its components are neither holomorphic nor
anti-holomorphic. We obtain the exact two- and three-point functions of this
current and a four-point function in the first two leading orders of a 1/k
expansion but to all orders in the deformation parameter. We further study the
operator product algebra of the currents, the equal time commutators and the
quantum equations of motion. The form of the equations of motion suggests the
existence of non-local charges which generate a Yangian. Possible applications
to string theory on Anti-de Sitter spaces and to condensed matter problems are
briefly discussed.Comment: 43 pages, Latex, one eps figure; v.2: minor corrections, a reference
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