Spectrum of elementary and collective excitations in the dimerized S=1/2 Heisenberg chain with frustration

TL;DR

This paper analyzes the low-energy excitations of a dimerized and frustrated antiferromagnetic Heisenberg chain using an analytic triplet-based approach, revealing bound states and calculating the spin structure factor with results matching numerical data.

Contribution

It introduces an analytic triplet quasiparticle approach for the excitation spectrum of the dimerized frustrated Heisenberg chain, including bound states and structure factor calculations.

Findings

Excellent agreement with exact diagonalization for δ > 0.1

Identification of singlet and triplet bound states

Calculation of contributions to the spin structure factor

Abstract

We have studied the low-energy excitation spectrum of a dimerized and frustrated antiferromagnetic Heisenberg chain. We use an analytic approach, based on a description of the excitations as triplets above a strong-coupling singlet ground state. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. Additional singlet (S=0) and triplet (S=1) modes are found as two-particle bound states of the elementary triplets. We have also calculated the contributions of the elementary and collective excitations into the spin structure factor. Our results are in excellent agreement with exact diagonalizations and dimer series expansions data as long as the dimerization parameter $\delta$ is not too small ($\delta>0.1$), i.e. while the elementary triplets can be treated as localized objects.