Question

Find the one-dimensional hamiltonian associated with the chiral Potts model by expanding the transfer matrix about the point in $\Gamma_\kappa \times \Gamma_\kappa$ where the Boltzmann weights are the identity. Carry out the expansion to second order, and investigate the second hamiltonian structure thus derived. Does the Reshetikhin criterion (exercise 2.8 ) apply to this case?

    Find the one-dimensional hamiltonian associated with the chiral Potts model by expanding the transfer matrix about the point in $\Gamma_\kappa \times \Gamma_\kappa$ where the Boltzmann weights are the identity. Carry out the expansion to second order, and investigate the second hamiltonian structure thus derived. Does the Reshetikhin criterion (exercise 2.8 ) apply to this case?

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Quantum Groups in Two-Dimensional Physics

Quantum Groups in Two-Dimensional Physics

Cisar Gómez, Martm… 1st Edition

Chapter 7, Problem 9

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Step 1

The model is defined on a lattice where each site can be in one of N states. The transfer matrix of the chiral Potts model is defined on a curve $\Gamma_\kappa$ in a complex projective space, where $\kappa$ is a parameter of the model. Step 2: Identify the point Show more…

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Find the one-dimensional hamiltonian associated with the chiral Potts model by expanding the transfer matrix about the point in $\Gamma_\kappa \times \Gamma_\kappa$ where the Boltzmann weights are the identity. Carry out the expansion to second order, and investigate the second hamiltonian structure thus derived. Does the Reshetikhin criterion (exercise 2.8 ) apply to this case?

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