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Phase diagram and two-particle structure of the $Z_3$-chiral Potts model | | G. von Gehlen
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8 Jul 1992 | | Subject: | hep-th | | Abstract: | We calculate the low-lying part of the spectrum of the $Z_3$-symmetrical chiral Potts quantum chain in its self-dual and integrable versions, using numerical diagonalisation of the hamiltonian for $N leq 12$ sites and extrapolation $N
a infty$. From the sequences of levels crossing we show that the massive phases have oscillatory correlation functions. We calculate the wave vector scaling exponent. In the high-temperature massive phase the pattern of the low-lying levels can be explained assuming the existence of two particles, with $Z_3$-charge $Q!=!1$ and $Q!=!2$, and their scattering states. In the superintegrable case the $Q!=!2$-particle has twice the mass of the $Q!=!1$-particle. Exponential convergence in $N$ is observed for the single particle gaps, while power convergence is seen for the scattering levels. In the high temperature limit of the self-dual model the parity violation in the particle dispersion relation is equivalent to the presence of a macroscopic momentum $P_m = pm vph/3$, where $vph$ is the chiral angle. | | Source: | arXiv, hep-th/9207022 | | Services: | Forum | Review | PDF | Favorites | |
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