## Abstract

We calculate the lowest translationally invariant levels of the Z{sub 3}- and Z{sub 4}-symmetrical chiral Potts quantum chains, using numerical diagonalization of the hamiltonian for N{<=}12 and N{<=}10 sites, respectively, and extrapolating N{yields}{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{sub n}-charges Q=1, ..., n-1 (mass m{sub Q}), and their scattering states. In the superintegrable case the masses of the n-1 particles become proportional to their respective charges: m{sub Q}=Qm{sub 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{sub 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{sub m}=(1-2Q/n){Phi}, where {Phi} is the chiral angle and Q is the Z{sub n}-charge of the respective particle. (orig.).

## Citation Formats

Gehlen, G von, and Honecker, A.
Multi-particle structure in the Z{sub n}-chiral Potts models.
Germany: N. p.,
1992.
Web.

Gehlen, G von, & Honecker, A.
Multi-particle structure in the Z{sub n}-chiral Potts models.
Germany.

Gehlen, G von, and Honecker, A.
1992.
"Multi-particle structure in the Z{sub n}-chiral Potts models."
Germany.

@misc{etde_10116733,

title = {Multi-particle structure in the Z{sub n}-chiral Potts models}

author = {Gehlen, G von, and Honecker, A}

abstractNote = {We calculate the lowest translationally invariant levels of the Z{sub 3}- and Z{sub 4}-symmetrical chiral Potts quantum chains, using numerical diagonalization of the hamiltonian for N{<=}12 and N{<=}10 sites, respectively, and extrapolating N{yields}{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{sub n}-charges Q=1, ..., n-1 (mass m{sub Q}), and their scattering states. In the superintegrable case the masses of the n-1 particles become proportional to their respective charges: m{sub Q}=Qm{sub 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{sub 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{sub m}=(1-2Q/n){Phi}, where {Phi} is the chiral angle and Q is the Z{sub n}-charge of the respective particle. (orig.).}

place = {Germany}

year = {1992}

month = {Oct}

}

title = {Multi-particle structure in the Z{sub n}-chiral Potts models}

author = {Gehlen, G von, and Honecker, A}

abstractNote = {We calculate the lowest translationally invariant levels of the Z{sub 3}- and Z{sub 4}-symmetrical chiral Potts quantum chains, using numerical diagonalization of the hamiltonian for N{<=}12 and N{<=}10 sites, respectively, and extrapolating N{yields}{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{sub n}-charges Q=1, ..., n-1 (mass m{sub Q}), and their scattering states. In the superintegrable case the masses of the n-1 particles become proportional to their respective charges: m{sub Q}=Qm{sub 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{sub 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{sub m}=(1-2Q/n){Phi}, where {Phi} is the chiral angle and Q is the Z{sub n}-charge of the respective particle. (orig.).}

place = {Germany}

year = {1992}

month = {Oct}

}