Dynamical correlations and quantum phase transition in the quantum Potts model

TL;DR

This paper investigates the finite temperature dynamical properties of the one-dimensional quantum Potts model, revealing diffusive decay behaviors and extending semiclassical analysis near quantum critical points, with implications for related quantum systems.

Contribution

It provides a detailed analysis of dynamical correlations in the quantum Potts model, including scattering matrices and decay functions, extending semiclassical methods near quantum phase transitions.

Findings

Correlation functions determined using conformal invariance in the critical regime

Decay functions exhibit diffusive behavior far from criticality

Semiclassical analysis remains valid at very low temperatures near the transition

Abstract

We present a detailed study of the finite temperature dynamical properties of the quantum Potts model in one dimension.Quasiparticle excitations in this model have internal quantum numbers, and their scattering matrix {\gf deep} in the gapped phases is shown to take a simple {\gf exchange} form in the perturbative regimes. The finite temperature correlation functions in the quantum critical regime are determined using conformal invariance, while {\gf far from the quantum critical point} we compute the decay functions analytically within a semiclassical approach of Sachdev and Damle [K. Damle and S. Sachdev, Phys. Rev. B \textbf{57}, 8307 (1998)]. As a consequence, decay functions exhibit a {\em diffusive character}. {\gf We also provide robust arguments that our semiclassical analysis carries over to very low temperatures even in the vicinity of the quantum phase transition.} Our results are also relevant for quantum rotor models, antiferromagnetic chains, and some spin ladder systems.