Elementary Excitations in Dimerized and Frustrated Heisenberg Chains

TL;DR

This paper provides a numerical analysis of low-energy excitations in frustrated, dimerized spin chains, revealing universal gap ratios and conditions for additional triplet branches, with implications for experimental materials.

Contribution

It offers new numerical insights into the excitation spectrum of frustrated and dimerized Heisenberg chains, including universal gap ratios and spectral branch splitting conditions.

Findings

Universal ratio of singlet to triplet gaps in the commensurate phase.

Conditions for splitting of a second triplet branch from the continuum.

Comparison with continuum field theory predictions.

Abstract

We present a detailed numerical analysis of the low energy excitation spectrum of a frustrated and dimerized spin $S=1/2$ Heisenberg chain. In particular, we show that in the commensurate spin--Peierls phase the ratio of the singlet and triplet excitation gap is a universal function which depends on the frustration parameter only. We identify the conditions for which a second elementary triplet branch in the excitation spectrum splits from the continuum. We compare our results with predictions from the continuum limit field theory . We discuss the relevance of our data in connection with recent experiments on $CuGeO_{3}$, $NaV_2O_5$, and $(VO)_2P_2O_7$.