Excitation spectrum of the S=1/2 quantum spin ladder with frustration: elementary quasiparticles and many-particle bound states

TL;DR

This paper investigates the complex excitation spectrum of a frustrated S=1/2 quantum spin ladder, revealing bound states, phase transitions, and the nature of quasiparticles using analytical and numerical methods.

Contribution

It introduces a detailed analysis of elementary and many-particle bound states in a frustrated spin ladder, highlighting the spectrum's complexity and the role of frustration.

Findings

Presence of low-lying singlet and triplet bound states

Binding energy increases with frustration

Spectrum becomes gapless near the phase transition

Abstract

We study the excitation spectrum of the two-chain S=1/2 Heisenberg spin ladder with additional inter-chain second-neighbor frustrating interactions. The one and two-particle excitations are analyzed by using a mapping of the model onto a Bose gas of hard-core triplets. We find that low-lying singlet and triplet two-particle bound states are present and their binding energy increases with increasing frustration. In addition, many-particle bound states are found by a combination of variational and exact diagonalization techniques. We prove that the larger the number of bound quasiparticles the larger the binding energy. Thus the excitation spectrum has a complex structure and consists of elementary triplets and collective many-particle singlet and triplet excitations which generally mix with the elementary ones. The model exhibits a quantum phase transition from an antiferromagnetic ladder phase (small frustration) into Haldane phase (effectively ferromagnetic ladder for large frustration). We argue that near the transition point the spectrum in both triplet and singlet channels becomes gapless. The excitation wave function is dominated by large-size bound states which leads to the vanishing of the quasiparticle residue.