Four State Models and Clifford Algebras

Abstract

With appropriate boundary conditions the anisotropic $XY$ chain in a magnetic field is known to be invariant under quantum group transformations. We generalize this model defining a class of integrable chains with several fermionic degrees of freedom per site. In order to maintain the quantum group symmetry a general condition on the parameters of these systems is derived. It is shown that the corresponding quantum algebra is a multi-parameter deformation of the Clifford algebra. Discussing a special physical example we observe a new type of zero modes.

16 pages + 2 uuencoded postscript figures, LaTeX

References in corpus (10)

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Cited by in corpus (3)

• The XX--model with boundaries. Part I: Diagonalization of the finite chain
• Spectra of non-hermitian quantum spin chains describing boundary induced phase transitions
• The exact equivalence of the one-flavour lattice Thirring model with Wilson fermions to a two-colour loop model