Spectral properties of the dimerized and frustrated $S=1/2$ chain

TL;DR

This paper uses continuous unitary transformations to analyze spectral densities in dimerized and frustrated S=1/2 chains, providing detailed predictions for experimental probes and revealing the limitations of the sine-Gordon model.

Contribution

It introduces a high-order perturbative method to compute spectral densities in dimerized and frustrated chains, linking microscopic models to experimental observables.

Findings

Spectral densities are computed for various dimerization and frustration levels.

Bound states and resonances significantly affect spectral continua.

The sine-Gordon model accurately describes low-energy features only at critical frustration.

Abstract

Spectral densities are calculated for the dimerized and frustrated S=1/2 chain using the method of continuous unitary transformations (CUTs). The transformation to an effective triplon model is realized in a perturbative fashion up to high orders about the limit of isolated dimers. An efficient description in terms of triplons (elementary triplets) is possible: a detailed analysis of the spectral densities is provided for strong and intermediate dimerization including the influence of frustration. Precise predictions are made for inelastic neutron scattering experiments probing the S=1 sector and for optical experiments (Raman scattering, infrared absorption) probing the S=0 sector. Bound states and resonances influence the important continua strongly. The comparison with the field theoretic results reveals that the sine-Gordon model describes the low-energy features for strong to intermediate dimerization only at critical frustration.