Reply to the "Comment on 'Neel order in doped quasi one-dimensional antiferromagnets'"

TL;DR

This paper clarifies the limitations of bosonization in describing doped quasi-one-dimensional antiferromagnets, demonstrating the crossover from low to high temperature and short to long length scales through analytical and numerical methods.

Contribution

It explicitly quantifies the validity limits of bosonization in antiferromagnetic chains by combining formulas and numerical analysis.

Findings

Bosonization is valid only at low temperatures and long lengths.

Crossover to high temperature/short length regime is characterized.

Numerical results support the analytical crossover analysis.

Abstract

In a recent comment by A.A. Zvyagin to our Letter [Phys. Rev. Lett. 89, 47202 (2002)] it was pointed out that the bosonization treatment of the antiferromagnetic Heisenberg chain is only valid in the low temperature and long length limit. We support this statement and quantify the limits of validity by explicitly showing the crossover to the high temperature and/or short length limit using a combination of bosonization formulas and numerical results.