Form factors in finite volume I: form factor bootstrap and truncated conformal space

TL;DR

This paper develops a non-perturbative method to analyze finite volume effects on matrix elements of local fields in integrable quantum field theories, confirming the form factor bootstrap through direct comparison with numerical approaches.

Contribution

It introduces a novel approach combining form factor bootstrap with truncated conformal space to accurately evaluate finite volume form factors across all volume ranges.

Findings

Confirmed the validity of the form factor bootstrap non-perturbatively.

Demonstrated the effectiveness of combining bootstrap and truncated conformal space methods.

Provided detailed volume dependence of matrix elements in tested models.

Abstract

We describe the volume dependence of matrix elements of local fields to all orders in inverse powers of the volume (i.e. only neglecting contributions that decay exponentially with volume). Using the scaling Lee-Yang model and the Ising model in a magnetic field as testing ground, we compare them to matrix elements extracted in finite volume using truncated conformal space approach to exact form factors obtained using the bootstrap method. We obtain solid confirmation for the form factor bootstrap, which is different from all previously available tests in that it is a non-perturbative and direct comparison of exact form factors to multi-particle matrix elements of local operators, computed from the Hamiltonian formulation of the quantum field theory. We also demonstrate that combining form factor bootstrap and truncated conformal space is an effective method for evaluating finite volume form factors in integrable field theories over the whole range in volume.