Operator Product Expansion on the Lattice: a Numerical Test in the Two-Dimensional Non-Linear Sigma-Model

TL;DR

This paper tests the operator product expansion in a two-dimensional lattice nonlinear sigma-model by comparing numerical results with perturbative predictions, finding good agreement within 5-10% error on small lattices.

Contribution

It provides the first numerical validation of the operator product expansion in a lattice nonlinear sigma-model using perturbative renormalization-group improved coefficients.

Findings

Perturbative OPE describes lattice data with 5-10% accuracy.

Good agreement observed on small lattices (m a ≈ 1/6).

Systematic errors are discussed in detail.

Abstract

We consider the short-distance behaviour of the product of the Noether O(N) currents in the lattice nonlinear sigma-model. We compare the numerical results with the predictions of the operator product expansion, using one-loop perturbative renormalization-group improved Wilson coefficients. We find that, even on quite small lattices (m a \approx 1/6), the perturbative operator product expansion describes that data with an error of 5-10% in a large window 2a \ltapprox x \ltapprox m^{-1}. We present a detailed discussion of the possible systematic errors.