A suggestion for an integrability notion for two dimensional spin systems

Details A suggestion for an integrability notion for two dimensional spin systems A suggestion for an integrability notion for two dimensional spin systems

2001-03-21

arxiv.org/abs/hep-th/0103176v1

Lett.Math.Phys. 55 (2001) 161-167

Physics

High Energy Physics

High Energy Physics - Theory

9 pages

Scientific paper

We suggest that trialgebraic symmetries migth be a sensible starting point for a notion of integrability for two dimensional spin systems. For a simple trialgebraic symmetry we give an explicit condition in terms of matrices which a Hamiltonian realizing such a symmetry has to satisfy and give an example of such a Hamiltonian which realizes a trialgebra recently given by the authors in another paper. Besides this, we also show that the same trialgebra can be realized on a kind of Fock space of q-oscillators, i.e. the suggested integrability concept gets via this symmetry a close connection to a kind of noncommutative quantum field theory, paralleling the relation between the integrability of spin chains and two dimensional conformal field theory.

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