Multi-particle structure in the Z_n-chiral Potts models

TL;DR

This paper investigates the low-energy spectrum of Z_n-chiral Potts quantum chains, revealing multi-particle structures and scattering behaviors, with implications for understanding integrable models and phase transitions.

Contribution

It provides numerical evidence for n-1 particle excitations and their scattering states in Z_n-chiral Potts models, extending understanding of their spectral properties.

Findings

Low-lying levels explained by n-1 particle charges and scattering states

Masses of particles proportional to their charges in superintegrable case

Exponential convergence for single particle gaps, power convergence for scattering levels

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)/\phi, where \phi is the chiral angle and Q is the Z_n-charge of the respective particle.