580 research outputs found
Wronskian-type formula for inhomogeneous TQ-equations
The transfer-matrix eigenvalues of the isotropic open Heisenberg quantum
spin-1/2 chain with non-diagonal boundary magnetic fields are known to satisfy
a TQ-equation with an inhomogeneous term. We derive here a discrete
Wronskian-type formula relating a solution of this inhomogeneous TQ-equation to
the corresponding solution of a dual inhomogeneous TQ-equation.Comment: 6 pages; to appear in Theor. Math. Phys. as part of the Proceedings
of the CQIS-2019 workshop in St. Petersbur
Inhomogeneous T-Q equation for the open XXX chain with general boundary terms: completeness and arbitrary spin
An inhomogeneous T-Q equation has recently been proposed by Cao, Yang, Shi
and Wang for the open spin-1/2 XXX chain with general (nondiagonal) boundary
terms. We argue that a simplified version of this equation describes all the
eigenvalues of the transfer matrix of this model. We also propose a generating
function for the inhomogeneous T-Q equations of arbitrary spin.Comment: 8 pages; v2: minor improvement
Supersymmetry in the boundary tricritical Ising field theory
We argue that it is possible to maintain both supersymmetry and integrability
in the boundary tricritical Ising field theory. Indeed, we find two sets of
boundary conditions and corresponding boundary perturbations which are both
supersymmetric and integrable. The first set corresponds to a ``direct sum'' of
two non-supersymmetric theories studied earlier by Chim. The second set
corresponds to a one-parameter deformation of another theory studied by Chim.
For both cases, the conserved supersymmetry charges are linear combinations of
Q, \bar Q and the spin-reversal operator \Gamma.Comment: 19 pages, LaTeX; amssymb, no figures; v2 one paragraph and one
reference added; v3 Erratum adde
Integrability + Supersymmetry + Boundary: Life on the edge is not so dull after all!
After a brief review of integrability, first in the absence and then in the
presence of a boundary, I outline the construction of actions for the N=1 and
N=2 boundary sine-Gordon models. The key point is to introduce Fermionic
boundary degrees of freedom in the boundary actions.Comment: 10 pages, LaTeX; requires ws-procs9x6.cls and rotating_pr.sty (World
Scientific proceedings style, 9 x 6 inch trim size); presented at "Deserfest:
A celebration of the life and works of Stanley Deser" in Ann Arbor, Michigan,
3-5 April 2004, and to appear in the Proceedings; v2 and v3 refs adde
Bethe Ansatz for the open XXZ chain from functional relations at roots of unity
We briefly review Bethe Ansatz solutions of the integrable open spin-1/2 XXZ
quantum spin chain derived from functional relations obeyed by the transfer
matrix at roots of unity.Comment: 10 pages, LaTeX; includes ws-procs9x6.cls and rotating_pr.sty (World
Scientific proceedings style, 9 x 6 inch trim size); presented at the 23rd
International Conference of Differential Geometric Methods in Theoretical
Physics (DGMTP) at the Nankai Institute of Mathematics in Tianjin, China,
20-26 August 2005, and to appear in the Proceeding
Bethe Ansatz solution of the open XX spin chain with nondiagonal boundary terms
We consider the integrable open XX quantum spin chain with nondiagonal
boundary terms. We derive an exact inversion identity, using which we obtain
the eigenvalues of the transfer matrix and the Bethe Ansatz equations. For
generic values of the boundary parameters, the Bethe Ansatz solution is
formulated in terms of Jacobian elliptic functions.Comment: 14 pages, LaTeX; amssymb, no figure
Algebraic Bethe ansatz for singular solutions
The Bethe equations for the isotropic periodic spin-1/2 Heisenberg chain with
N sites have solutions containing i/2, -i/2 that are singular: both the
corresponding energy and the algebraic Bethe ansatz vector are divergent. Such
solutions must be carefully regularized. We consider a regularization involving
a parameter that can be determined using a generalization of the Bethe
equations. These generalized Bethe equations provide a practical way of
determining which singular solutions correspond to eigenvectors of the model.Comment: 10 pages; v2: refs added; v3: new section on general singular
solutions, and more reference
Twisting singular solutions of Bethe's equations
The Bethe equations for the periodic XXX and XXZ spin chains admit singular
solutions, for which the corresponding eigenvalues and eigenvectors are
ill-defined. We use a twist regularization to derive conditions for such
singular solutions to be physical, in which case they correspond to genuine
eigenvalues and eigenvectors of the Hamiltonian.Comment: 10 pages; v2: references added; v3: introduction expanded, and more
references adde
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