Four State Models and Clifford Algebras

TL;DR

This paper introduces a generalized class of integrable quantum chains with multiple fermionic degrees of freedom, revealing a multi-parameter deformed Clifford algebra structure and identifying new zero modes.

Contribution

It extends the anisotropic XY model to more complex chains with quantum group symmetry and characterizes the associated algebraic structure.

Findings

Identification of a multi-parameter deformed Clifford algebra

Discovery of a new type of zero modes

General condition for quantum group invariance

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.