Quantum chains with a Catalan tree pattern of conserved charges: the $\Delta =-1$ XXZ model and the isotropic octonionic chain

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 $\Delta =-1$. 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.

20 pages in plain TeX; uses macro harvmac

References in corpus (2)

• Structure of the conservation laws in integrable spin chains with short range interactions
• Quantum Integrals of Motion for the Heisenberg Spin Chain

Cited by in corpus (8)

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• Conserved charges of non-yangian type for the Frahm-Polychronakos spin chain
• On integrable matrix product operators with bond dimension $D=4$
• Division Algebras and Extended N=2,4,8 SuperKdVs
• Spin Angular Momentum of Proton Spin Puzzle in Complex Octonion Spaces