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arXiv · hep-th/9210125

Multi-particle structure in the Z_n-chiral Potts models

G. von Gehlen·A. Honecker
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Abstract

We calculate the lowest translationally invariant levels of the Z_3- and Z_4-symmetrical chiral Potts quantum chains, using numerical diagonalization of the hamiltonian for N <= 12 and N <= 10 sites, respectively, and extrapolating N to infinity. In the high-temperature massive phase we find that the pattern of the low-lying zero momentum levels can be explained assuming the existence of n-1 particles carrying Z_n-charges Q = 1, ... , n-1 (mass m_Q), and their scattering states. In the superintegrable case the masses of the n-1 particles become proportional to their respective charges: m_Q = Q m_1. Exponential convergence in N is observed for the single particle gaps, while power convergence is seen for the scattering levels. We also verify that qualitatively the same pattern appears for the self-dual and integrable cases. For general Z_n we show that the energy-momentum relations of the particles show a parity non-conservation asymmetry which for very high temperatures is exclusive due to the presence of a macroscopic momentum P_m=(1-2Q/n)/ϕ, where ϕis the chiral angle and Q is the Z_n-charge of the respective particle.

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G. von Gehlen, A. Honecker. 1992-10-22. Multi-particle structure in the Z_n-chiral Potts models. https://doi.org/10.1088/0305-4470%2F26%2F6%2F012

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