68 research outputs found
Finite-size correction and bulk hole-excitations for special case of an open XXZ chain with nondiagonal boundary terms at roots of unity
Using our solution for the open spin-1/2 XXZ quantum spin chain with N spins
and two arbitrary boundary parameters at roots of unity, the central charge and
the conformal dimensions for bulk hole excitations are derived from the 1/N
correction to the energy (Casimir energy).Comment: 21 pages, LaTeX, v2: minor changes and 3 references adde
Boundary energy of the general open XXZ chain at roots of unity
We have recently proposed a Bethe Ansatz solution of the open spin-1/2 XXZ
quantum spin chain with general integrable boundary terms (containing six free
boundary parameters) at roots of unity. We use this solution, together with an
appropriate string hypothesis, to compute the boundary energy of the chain in
the thermodynamic limit.Comment: 22 pages, 6 figures; v2: some comments, a reference and a footnote
adde
Exact solution of the open XXZ chain with general integrable boundary terms at roots of unity
We propose a Bethe-Ansatz-type solution of the open spin-1/2 integrable XXZ
quantum spin chain with general integrable boundary terms and bulk anisotropy
values i \pi/(p+1), where p is a positive integer. All six boundary parameters
are arbitrary, and need not satisfy any constraint. The solution is in terms of
generalized T - Q equations, having more than one Q function. We find numerical
evidence that this solution gives the complete set of 2^N transfer matrix
eigenvalues, where N is the number of spins.Comment: 22 page
Generalized T-Q relations and the open spin-s XXZ chain with nondiagonal boundary terms
We consider the open spin-s XXZ quantum spin chain with nondiagonal boundary
terms. By exploiting certain functional relations at roots of unity, we derive
a generalized form of T-Q relation involving more than one independent Q(u),
which we use to propose the Bethe-ansatz-type expressions for the eigenvalues
of the transfer matrix. At most two of the boundary parameters are set to be
arbitrary and the bulk anisotropy parameter has values \eta = i\pi/2,
i\pi/4,... We also provide numerical evidence for the completeness of the
Bethe-ansatz-type solutions derived, using s = 1 case as an example.Comment: 23 pages. arXiv admin note: substantial text overlap with
arXiv:0901.3558; v2: published versio
Generalized T-Q relations and the open XXZ chain
We propose a generalization of the Baxter T-Q relation which involves more
than one independent Q(u). We argue that the eigenvalues of the transfer matrix
of the open XXZ quantum spin chain are given by such generalized T-Q relations,
for the case that at most two of the boundary parameters {\alpha_-, \alpha_+,
\beta_-, \beta_+} are nonzero, and the bulk anisotropy parameter has values
\eta = i \pi/2, i\pi/4, ...Comment: 14 pages, LaTeX; amssymb, no figure
Complete Bethe Ansatz solution of the open spin-s XXZ chain with general integrable boundary terms
We consider the open spin-s XXZ quantum spin chain with N sites and general
integrable boundary terms for generic values of the bulk anisotropy parameter,
and for values of the boundary parameters which satisfy a certain constraint.
We derive two sets of Bethe Ansatz equations, and find numerical evidence that
together they give the complete set of eigenvalues of the transfer
matrix. For the case s=1, we explicitly determine the Hamiltonian, and find an
expression for its eigenvalues in terms of Bethe roots.Comment: 23 pages -- Latex2e; misprints in appendix correcte
Structure of the two-boundary XXZ model with non-diagonal boundary terms
We study the integrable XXZ model with general non-diagonal boundary terms at
both ends. The Hamiltonian is considered in terms of a two boundary extension
of the Temperley-Lieb algebra.
We use a basis that diagonalizes a conserved charge in the one-boundary case.
The action of the second boundary generator on this space is computed. For the
L-site chain and generic values of the parameters we have an irreducible space
of dimension 2^L. However at certain critical points there exists a smaller
irreducible subspace that is invariant under the action of all the bulk and
boundary generators. These are precisely the points at which Bethe Ansatz
equations have been formulated. We compute the dimension of the invariant
subspace at each critical point and show that it agrees with the splitting of
eigenvalues, found numerically, between the two Bethe Ansatz equations.Comment: 9 pages Latex. Minor correction
Equivalences between spin models induced by defects
The spectrum of integrable spin chains are shown to be independent of the
ordering of their spins. As an application we introduce defects (local spin
inhomogeneities in homogenous chains) in two-boundary spin systems and, by
changing their locations, we show the spectral equivalence of different
boundary conditions. In particular we relate certain nondiagonal boundary
conditions to diagonal ones.Comment: 14 pages, 16 figures, LaTeX, Extended versio
Construction of a Coordinate Bethe Ansatz for the asymmetric simple exclusion process with open boundaries
The asymmetric simple exclusion process with open boundaries, which is a very
simple model of out-of-equilibrium statistical physics, is known to be
integrable. In particular, its spectrum can be described in terms of Bethe
roots. The large deviation function of the current can be obtained as well by
diagonalizing a modified transition matrix, that is still integrable: the
spectrum of this new matrix can be also described in terms of Bethe roots for
special values of the parameters. However, due to the algebraic framework used
to write the Bethe equations in the previous works, the nature of the
excitations and the full structure of the eigenvectors were still unknown. This
paper explains why the eigenvectors of the modified transition matrix are
physically relevant, gives an explicit expression for the eigenvectors and
applies it to the study of atypical currents. It also shows how the coordinate
Bethe Ansatz developped for the excitations leads to a simple derivation of the
Bethe equations and of the validity conditions of this Ansatz. All the results
obtained by de Gier and Essler are recovered and the approach gives a physical
interpretation of the exceptional points The overlap of this approach with
other tools such as the matrix Ansatz is also discussed. The method that is
presented here may be not specific to the asymmetric exclusion process and may
be applied to other models with open boundaries to find similar exceptional
points.Comment: references added, one new subsection and corrected typo
Non-diagonal reflection for the non-critical XXZ model
The most general physical boundary -matrix for the open XXZ spin chain in
the non-critical regime () is derived starting from the bare
Bethe ansazt equations. The boundary -matrix as expected is expressed in
terms of -functions. In the isotropic limit corresponding results for
the open XXX chain are also reproduced.Comment: 8 pages Late
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