Kinks in Finite Volume

TL;DR

This paper develops a method to calculate multi-kink energy levels in finite volume for integrable (1+1)-dimensional quantum field theories with degenerate vacua, and validates it against numerical results for the tricritical Ising model.

Contribution

It introduces a technique to compute finite-volume multi-kink energies using the factorizable S-matrix in integrable theories, with applications to the tricritical Ising model.

Findings

Analytical predictions match numerical results for kink scattering theories.

The method distinguishes between different proposed S-matrices for the subleading magnetic perturbation.

Exact calculations are feasible up to exponentially suppressed off-shell and tunneling effects.

Abstract

A (1+1)-dimensional quantum field theory with a degenerate vacuum (in infinite volume) can contain particles, known as kinks, which interpolate between different vacua and have nontrivial restrictions on their multi-particle Hilbert space. Assuming such a theory to be integrable, we show how to calculate the multi-kink energy levels in finite volume given its factorizable $S$-matrix. In massive theories this can be done exactly up to contributions due to off-shell and tunneling effects that fall off exponentially with volume. As a first application we compare our analytical predictions for the kink scattering theories conjectured to describe the subleading thermal and magnetic perturbations of the tricritical Ising model with numerical results from the truncated conformal space approach. In particular, for the subleading magnetic perturbation our results allow us to decide between the two different $S$-matrices proposed by Smirnov and Zamolodchikov.