Low-Temperature Expansions and Correlation Functions of the Z_3-Chiral Potts Model

TL;DR

This paper uses perturbative methods to analyze the spectrum and correlation functions of the Z_3-chiral Potts quantum chain in the low-temperature phase, revealing spectral similarities with the high-temperature phase and insights into correlation oscillations.

Contribution

It provides new perturbative results for the spectrum and correlation functions of the Z_3-chiral Potts model, including explicit calculations and insights into oscillatory behavior.

Findings

Spectrum in low-temperature phase matches high-temperature phase with interchanged roles.

Ground state and first excitations approximated accurately.

Correlation functions may exhibit oscillations with estimated lengths.

Abstract

Using perturbative methods we derive new results for the spectrum and correlation functions of the general Z_3-chiral Potts quantum chain in the massive low-temperature phase. Explicit calculations of the ground state energy and the first excitations in the zero momentum sector give excellent approximations and confirm the general statement that the spectrum in the low-temperature phase of general Z_n-spin quantum chains is identical to one in the high-temperature phase where the role of charge and boundary conditions are interchanged. Using a perturbative expansion of the ground state for the Z_3 model we are able to gain some insight in correlation functions. We argue that they might be oscillating and give estimates for the oscillation length as well as the correlation length.