Quantum chains with a Catalan tree pattern of conserved charges: the Δ= -1 XXZ model and the isotropic octonionic chain
M. P. Grabowski, P. Mathieu
Abstract
A class of quantum chains possessing a family of local conserved charges with a Catalan tree pattern is studied. Recently, we have identified such a structure in the integrable SU(N)-invariant chains. In the present work we find sufficient conditions for the existence of a family of charges with this structure in terms of the underlying algebra. Two additional systems with a Catalan tree structure of conserved charges are found. One is the spin 1/2 XXZ model with Δ=-1. The other is a new octonionic isotropic chain, generalizing the Heisenberg model. This system provides an interesting example of an infinite family of noncommuting local conserved quantities.
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