On the Two-Point Correlation Function for the $U_q[SU(2)]$ Invariant Spin One-Half Heisenberg Chain at Roots of Unity

Abstract

Using $U_q[SU(2)]$ tensor calculus we compute the two-point scalar operators (TPSO), their averages on the ground-state give the two-point correlation functions. The TPSOs are identified as elements of the Temperley-Lieb algebra and a recurrence relation is given for them. We have not tempted to derive the analytic expressions for the correlation functions in the general case but got some partial results. For $q=e^{i\pi /3}$, all correlation functions are (trivially) zero, for $q=e^{i\pi /4}$, they are related in the continuum to the correlation functions of left-handed and right-handed Majorana fields in the half plane coupled by the boundary condition. In the case $q=e^{i\pi /6}$, one gets the correlation functions of Mittag's and Stephen's parafermions for the three-state Potts model. A diagrammatic approach to compute correlation functions is also presented.

19 pages, LaTeX, BONN-HE-93-35

References in corpus (3)

• Correlation Functions of the XXZ model for $\Delta <-1$
• Bethe Ansatz and Quantum Groups: The Light--Cone Approach. II. From RSOS($p+1$) models to $p-$restricted Sine--Gordon Field Theories
• Quantum Groups, Correlation Functions and Infrared Divergences

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• PT Symmetry on the Lattice: The Quantum Group Invariant XXZ Spin-Chain
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• Finite lattice Bethe ansatz systems and the Heun equation
• On the Construction of Correlation Functions for the Integrable Supersymmetric Fermion Models
• NUMERICAL INVESTIGATION OF CORRELATION FUNCTIONS FOR THE U_qSU(2) INVARIANT SPIN-1/2 HEISENBERG CHAIN
• Temperley-Lieb Words as Valence-Bond Ground States