47 research outputs found
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
The XXZ model with anti-periodic twisted boundary conditions
We derive functional equations for the eigenvalues of the XXZ model subject
to anti-diagonal twisted boundary conditions by means of fusion of transfer
matrices and by Sklyanin's method of separation of variables. Our findings
coincide with those obtained using Baxter's method and are compared to the
recent solution of Galleas. As an application we study the finite size scaling
of the ground state energy of the model in the critical regime.Comment: 22 pages and 3 figure
Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries
We analyze the Bethe ansatz equations describing the complete spectrum of the
transition matrix of the partially asymmetric exclusion process on a finite
lattice and with the most general open boundary conditions. We extend results
obtained recently for totally asymmetric diffusion [J. de Gier and F.H.L.
Essler, J. Stat. Mech. P12011 (2006)] to the case of partial symmetry. We
determine the finite-size scaling of the spectral gap, which characterizes the
approach to stationarity at large times, in the low and high density regimes
and on the coexistence line. We observe boundary induced crossovers and discuss
possible interpretations of our results in terms of effective domain wall
theories.Comment: 30 pages, 9 figures, typeset for pdflatex; revised versio
Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
We derive the Bethe ansatz equations describing the complete spectrum of the
transition matrix of the partially asymmetric exclusion process with the most
general open boundary conditions. By analysing these equations in detail for
the cases of totally asymmetric and symmetric diffusion, we calculate the
finite-size scaling of the spectral gap, which characterizes the approach to
stationarity at large times. In the totally asymmetric case we observe boundary
induced crossovers between massive, diffusive and KPZ scaling regimes. We
further study higher excitations, and demonstrate the absence of oscillatory
behaviour at large times on the ``coexistence line'', which separates the
massive low and high density phases. In the maximum current phase, oscillations
are present on the KPZ scale . While independent of the
boundary parameters, the spectral gap as well as the oscillation frequency in
the maximum current phase have different values compared to the totally
asymmetric exclusion process with periodic boundary conditions. We discuss a
possible interpretation of our results in terms of an effective domain wall
theory.Comment: 42 pages, 25 figures; added appendix and minor correction
Drinfeld twist and symmetric Bethe vectors of the open XYZ chain with non-diagonal boundary terms
With the help of the Drinfeld twist or factorizing F-matrix for the
eight-vertex solid-on-solid (SOS) model, we find that in the F-basis provided
by the twist the two sets of pseudo-particle creation operators simultaneously
take completely symmetric and polarization free form. This allows us to obtain
the explicit and completely symmetric expressions of the two sets of Bethe
states of the model.Comment: Latex file, 25 page
Non-diagonal open spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and matrix elements of some quasi-local operators
The integrable quantum models, associated to the transfer matrices of the
6-vertex reflection algebra for spin 1/2 representations, are studied in this
paper. In the framework of Sklyanin's quantum separation of variables (SOV), we
provide the complete characterization of the eigenvalues and eigenstates of the
transfer matrix and the proof of the simplicity of the transfer matrix
spectrum. Moreover, we use these integrable quantum models as further key
examples for which to develop a method in the SOV framework to compute matrix
elements of local operators. This method has been introduced first in [1] and
then used also in [2], it is based on the resolution of the quantum inverse
problem (i.e. the reconstruction of all local operators in terms of the quantum
separate variables) plus the computation of the action of separate covectors on
separate vectors. In particular, for these integrable quantum models, which in
the homogeneous limit reproduce the open spin-1/2 XXZ quantum chains with
non-diagonal boundary conditions, we have obtained the SOV-reconstructions for
a class of quasi-local operators and determinant formulae for the
covector-vector actions. As consequence of these findings we provide one
determinant formulae for the matrix elements of this class of reconstructed
quasi-local operators on transfer matrix eigenstates.Comment: 40 pages. Minor modifications in the text and some notations and some
more reference adde
A deformed analogue of Onsager's symmetry in the XXZ open spin chain
The XXZ open spin chain with general integrable boundary conditions is shown
to possess a q-deformed analogue of the Onsager's algebra as fundamental
non-abelian symmetry which ensures the integrability of the model. This
symmetry implies the existence of a finite set of independent mutually
commuting nonlocal operators which form an abelian subalgebra. The transfer
matrix and local conserved quantities, for instance the Hamiltonian, are
expressed in terms of these nonlocal operators. It follows that Onsager's
original approach of the planar Ising model can be extended to the XXZ open
spin chain.Comment: 12 pages; LaTeX file with amssymb; v2: typos corrected,
clarifications in the text; v3: minor changes in references, version to
appear in JSTA
Coideal Quantum Affine Algebra and Boundary Scattering of the Deformed Hubbard Chain
We consider boundary scattering for a semi-infinite one-dimensional deformed
Hubbard chain with boundary conditions of the same type as for the Y=0 giant
graviton in the AdS/CFT correspondence. We show that the recently constructed
quantum affine algebra of the deformed Hubbard chain has a coideal subalgebra
which is consistent with the reflection (boundary Yang-Baxter) equation. We
derive the corresponding reflection matrix and furthermore show that the
aforementioned algebra in the rational limit specializes to the (generalized)
twisted Yangian of the Y=0 giant graviton.Comment: 21 page. v2: minor correction
Central extension of the reflection equations and an analog of Miki's formula
Two different types of centrally extended quantum reflection algebras are
introduced. Realizations in terms of the elements of the central extension of
the Yang-Baxter algebra are exhibited. A coaction map is identified. For the
special case of , a realization in terms of elements
satisfying the Zamolodchikov-Faddeev algebra - a `boundary' analog of Miki's
formula - is also proposed, providing a free field realization of
(q-Onsager) currents.Comment: 11 pages; two references added; to appear in J. Phys.
Asymptotic Bethe equations for open boundaries in planar AdS/CFT
We solve, by means of a nested coordinate Bethe ansatz, the open-boundaries
scattering theory describing the excitations of a free open string propagating
in , carrying large angular momentum , and ending on
a maximal giant graviton whose angular momentum is in the same plane. We thus
obtain the all-loop Bethe equations describing the spectrum, for finite but
large, of the energies of such strings, or equivalently, on the gauge side of
the AdS/CFT correspondence, the anomalous dimensions of certain operators built
using the epsilon tensor of SU(N). We also give the Bethe equations for strings
ending on a probe D7-brane, corresponding to meson-like operators in an
gauge theory with fundamental matter.Comment: 30 pages. v2: minor changes and discussion section added, J.Phys.A
version