1,734 research outputs found
Exceptional solutions to the eight-vertex model and integrability of anisotropic extensions of massive fermionic models
We consider several anisotropic extensions of the Belavin model, and show
that integrability holds also for the massive case for some specific relations
between the coupling constants. This is done by relating the S-matrix
factorization property to the exceptional solutions of the eight-vertex model.
The relation of exceptional solutions to the XXZ and six-vertex models is also
shown
Thermodynamics of the quantum Landau-Lifshitz model
We present thermodynamics of the quantum su(1,1) Landau-Lifshitz model,
following our earlier exposition [J. Math. Phys. 50, 103518 (2009)] of the
quantum integrability of the theory, which is based on construction of
self-adjoint extensions, leading to a regularized quantum Hamiltonian for an
arbitrary n-particle sector. Starting from general discontinuity properties of
the functions used to construct the self-adjoint extensions, we derive the
thermodynamic Bethe Ansatz equations. We show that due to non-symmetric and
singular kernel, the self-consistency implies that only negative chemical
potential values are allowed, which leads to the conclusion that, unlike its
su(2) counterpart, the su(1,1) LL theory at T=0 has no instabilities.Comment: 10 page
Higher charges and regularized quantum trace identities in su(1,1) Landau-Lifshitz model
We solve the operator ordering problem for the quantum continuous integrable
su(1,1) Landau-Lifshitz model, and give a prescription to obtain the quantum
trace identities, and the spectrum for the higher-order local charges. We also
show that this method, based on operator regularization and renormalization,
which guarantees quantum integrability, as well as the construction of
self-adjoint extensions, can be used as an alternative to the discretization
procedure, and unlike the latter, is based only on integrable representations.Comment: 27 pages; misprints corrected, references adde
Quantum integrability of the Alday-Arutyunov-Frolov model
We investigate the quantum integrability of the Alday-Arutyunov-Frolov (AAF)
model by calculating the three-particle scattering amplitude at the first
non-trivial order and showing that the S-matrix is factorizable at this order.
We consider a more general fermionic model and find a necessary constraint to
ensure its integrability at quantum level. We then show that the quantum
integrability of the AAF model follows from this constraint. In the process, we
also correct some missed points in earlier works.Comment: 40 pages; Replaced with published version. Appendix and comments
adde
The r-matrix of the Alday-Arutyunov-Frolov model
We investigate the classical integrability of the Alday-Arutyunov-Frolov model, and show that the Lax connection can be reduced to a simpler 2 x 2 representation. Based on this result, we calculate the algebra between the L-operators and find that it has a highly non-ultralocal form. We then employ and make a suitable generalization of the regularization technique proposed by Mail let for a simpler class of non-ultralocal models, and find the corresponding r- and s-matrices. We also make a connection between the operator-regularization method proposed earlier for the quantum case, and the Mail let's symmetric limit regularization prescription used for non-ultralocal algebras in the classical theory.CAPESFAPESP [2011/20242-3
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