2,501 research outputs found
Exact solution of the trigonometric SU(3) spin chain with generic off-diagonal boundary reflections
The nested off-diagonal Bethe ansatz is generalized to study the quantum spin
chain associated with the R-matrix and generic integrable
non-diagonal boundary conditions. By using the fusion technique, certain closed
operator identities among the fused transfer matrices at the inhomogeneous
points are derived. The corresponding asymptotic behaviors of the transfer
matrices and their values at some special points are given in detail. Based on
the functional analysis, a nested inhomogeneous T-Q relations and Bethe ansatz
equations of the system are obtained. These results can be naturally
generalized to cases related to the algebra.Comment: published version, 27 pages, 1 table, 1 figur
A representation basis for the quantum integrable spin chain associated with the su(3) algebra
An orthogonal basis of the Hilbert space for the quantum spin chain
associated with the su(3) algebra is introduced. Such kind of basis could be
treated as a nested generalization of separation of variables (SoV) basis for
high-rank quantum integrable models. It is found that all the monodromy-matrix
elements acting on a basis vector take simple forms. With the help of the
basis, we construct eigenstates of the su(3) inhomogeneous spin torus (the
trigonometric su(3) spin chain with antiperiodic boundary condition) from its
spectrum obtained via the off-diagonal Bethe Ansatz (ODBA). Based on small
sites (i.e. N=2) check, it is conjectured that the homogeneous limit of the
eigenstates exists, which gives rise to the corresponding eigenstates of the
homogenous model.Comment: 24 pages, no figure, published versio
Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms
The Izergin-Korepin model with general non-diagonal boundary terms, a typical
integrable model beyond A-type and without U(1)-symmetry, is studied via the
off-diagonal Bethe ansatz method. Based on some intrinsic properties of the
R-matrix and the K-matrices, certain operator product identities of the
transfer matrix are obtained at some special points of the spectral parameter.
These identities and the asymptotic behaviors of the transfer matrix together
allow us to construct the inhomogeneous T-Q relation and the associated Bethe
ansatz equations. In the diagonal boundary limit, the reduced results coincide
exactly with those obtained via other methods.Comment: 24 pages, published versio
A convenient basis for the Izergin-Korepin model
We propose a convenient orthogonal basis of the Hilbert space for the
Izergin-Korepin model (or the quantum spin chain associated with the
algebra). It is shown that the monodromy-matrix elements acting
on the basis take relatively simple forms (c.f. acting on the original basis ),
which is quite similar as that in the so-called F-basis for the quantum spin
chains associated with -type (super)algebras. As an application, we present
the recursive expressions of Bethe states in the basis for the Izergin-Korepin
model.Comment: 24 pages, no figure
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