Asymptotic scattering and duality in the one-dimensional three-state quantum Potts model on a lattice

TL;DR

This paper uses numerical methods to analyze the low-energy spectrum and asymptotic scattering properties of quasiparticles in the one-dimensional three-state quantum Potts model, revealing insights into its effective field theory near criticality.

Contribution

It provides a numerical determination of the quasiparticle spectrum and asymptotic S-matrix, connecting lattice results with effective field theory predictions.

Findings

Finite size spectrum matches an effective model.

Asymptotic S-matrix exhibits exchange form below a momentum scale.

The momentum scale p* vanishes faster than the Compton scale near criticality.

Abstract

We determine numerically the single-particle and the two-particle spectrum of the three-state quantum Potts model on a lattice by using the density matrix renormalization group method, and extract information on the asymptotic (small momentum) S-matrix of the quasiparticles. The low energy part of the finite size spectrum can be understood in terms of a simple effective model introduced in a previous work, and is consistent with an asymptotic S-matrix of an exchange form below a momentum scale $p^*$. This scale appears to vanish faster than the Compton scale, $mc$, as one approaches the critical point, suggesting that a dangerously irrelevant operator may be responsible for the behavior observed on the lattice.