Quantitative expression of the spin gap via bosonization for a dimerized spin-1/2 chain

TL;DR

This paper derives a quantitative formula for the spin gap in a dimerized spin-1/2 chain using bosonization, sine-Gordon model results, and renormalization group analysis, aligning well with numerical data.

Contribution

It provides a new, precise analytical expression for the spin gap in dimerized spin chains, incorporating marginal perturbations.

Findings

The derived formula matches numerical estimates.

Inclusion of marginally irrelevant perturbations improves accuracy.

The approach bridges field theory and numerical results.

Abstract

Using results on the mass gap in the sine-Gordon model combined with the exact amplitudes in the bosonized representation of the Heisenberg spin-1/2 chain and one-loop renormalization group, we derive a quantitative expression for the gap in a dimerized spin-1/2 chain. This expression is shown to be in good agreement with recent numerical estimates when a marginally irrelevant perturbation is taken into account.