From deconfined spinons to coherent magnons in an antiferromagnetic Heisenberg chain with long range interactions

TL;DR

This paper investigates how long-range interactions in an antiferromagnetic Heisenberg chain lead to a transition from deconfined spinons to coherent magnons, revealing the emergence of long-range order and bound states.

Contribution

It introduces a combined numerical and analytical study of long-range antiferromagnetic chains, showing the transition from spin liquid to ordered phases and the formation of coherent magnons.

Findings

Long-range interactions induce long-range antiferromagnetic order.

Bound states of spinons form coherent magnons at weak interactions.

The spin dynamical structure factor reveals quasiparticle bands emerging from the two-spinon continuum.

Abstract

We study the spectrum and the nature of the excitations of an antiferromagnetic (AFM) Heisenberg chain with staggered long range interactions, both numerically using the time-dependent density matrix renormalization group (tDMRG) method and by means of a multi-spinon approximation that qualitatively explains its main features. The unfrustrated long-range nature of the exchange effectively increases the dimensionality of the system and the chain is able to undergo true symmetry breaking and develop long range order, transitioning from a gapless spin liquid to a gapless ordered AFM phase. We calculated the momentum resolved spin dynamical structure factor and found that for weakly decaying interactions the emergence of N\'eel order can be associated to the formation of bound states of spinons that become coherent magnons. The quasiparticle band leaks out from the two-spinon continuum that is pushed up to higher energies. Our physical picture is also supported by an analysis of the behavior of the excitations in real-time.