Does the XY Model have an integrable continuum limit?

TL;DR

This paper investigates whether the XY model's continuum limit is integrable by comparing non-perturbative results from the form factor bootstrap and lattice formulations, revealing new sectors and decay behaviors.

Contribution

It introduces a new parafermionic superselection sector in the bootstrap approach and tests a recent prediction about lattice artifact decay in the XY model.

Findings

Discovery of a new parafermionic superselection sector.

Validation of logarithmic decay of lattice artifacts.

Comparison of S-matrix and correlation functions across methods.

Abstract

The quantum field theory describing the massive O(2) nonlinear sigma-model is investigated through two non-perturbative constructions: The form factor bootstrap based on integrability and the lattice formulation as the XY model. The S-matrix, the spin and current two-point functions, as well as the 4-point coupling are computed and critically compared in both constructions. On the bootstrap side a new parafermionic super selection sector is found; in the lattice theory a recent prediction for the (logarithmic) decay of lattice artifacts is probed.