13 research outputs found
Yang-Baxter equation for the asymmetric eight-vertex model
In this note we study `a la Baxter [1] the possible integrable manifolds of
the asymmetric eight-vertex model. As expected they occur when the Boltzmann
weights are either symmetric or satisfy the free-fermion condition but our
analysis clarify the reason both manifolds need to share a universal invariant.
We also show that the free-fermion condition implies three distinct classes of
integrable models.Comment: Latex, 12 pages, 1 figur
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
Revisiting the Y=0 open spin chain at one loop
In 2005, Berenstein and Vazquez determined an open spin chain Hamiltonian
describing the one-loop anomalous dimensions of determinant-like operators
corresponding to open strings attached to Y=0 maximal giant gravitons. We
construct the transfer matrix (generating functional of conserved quantities)
containing this Hamiltonian, thereby directly proving its integrability. We
find the eigenvalues of this transfer matrix and the corresponding Bethe
equations, which we compare with proposed all-loop Bethe equations. We note
that the Bethe ansatz solution has a certain "gauge" freedom, and is not
completely unique.Comment: 16 page