4 research outputs found
Graded reflection equation algebras and integrable Kondo impurities in the one-dimensional t-J model
Integrable Kondo impurities in two cases of the one-dimensional model
are studied by means of the boundary -graded quantum inverse
scattering method. The boundary matrices depending on the local magnetic
moments of the impurities are presented as nontrivial realizations of the
reflection equation algebras in an impurity Hilbert space. Furthermore, these
models are solved by using the algebraic Bethe ansatz method and the Bethe
ansatz equations are obtained.Comment: 14 pages, RevTe
Integrable Kondo impurities in one-dimensional extended Hubbard models
Three kinds of integrable Kondo problems in one-dimensional extended Hubbard models are studied by means of the boundary graded quantum inverse scattering method. The boundary K matrices depending on the local moments of the impurities are presented as a nontrivial realization of the graded reflection equation algebras acting in a (2s alpha + 1)-dimensional impurity Hilbert space. Furthermore, these models are solved using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained
The open XXZ and associated models at q root of unity
The generalized open XXZ model at root of unity is considered. We review
how associated models, such as the harmonic oscillator, and the lattice
sine-Gordon and Liouville models are obtained. Explicit expressions of the
local Hamiltonian of the spin XXZ spin chain coupled to dynamical
degrees of freedom at the one end of the chain are provided. Furthermore, the
boundary non-local charges are given for the lattice sine Gordon model and the
harmonic oscillator with open boundaries. We then identify the spectrum and
the corresponding Bethe states, of the XXZ and the q harmonic oscillator in the
cyclic representation with special non diagonal boundary conditions. Moreover,
the spectrum and Bethe states of the lattice versions of the sine-Gordon and
Liouville models with open diagonal boundaries is examined. The role of the
conserved quantities (boundary non-local charges) in the derivation of the
spectrum is also discussed.Comment: 31 pages, LATEX, minor typos correcte
Analytical Bethe Ansatz for closed and open gl(n)-spin chains in any representation
We present an "algebraic treatment" of the analytical Bethe Ansatz. For this
purpose, we introduce abstract monodromy and transfer matrices which provide an
algebraic framework for the analytical Bethe Ansatz. It allows us to deal with
a generic gl(n)-spin chain possessing on each site an arbitrary
gl(n)-representation. For open spin chains, we use the classification of the
reflection matrices to treat all the diagonal boundary cases. As a result, we
obtain the Bethe equations in their full generality for closed and open spin
chains. The classifications of finite dimensional irreducible representations
for the Yangian (closed spin chains) and for the reflection algebras (open spin
chains) are directly linked to the calculation of the transfer matrix
eigenvalues. As examples, we recover the usual closed and open spin chains, we
treat the alternating spin chains and the closed spin chain with impurity