Fractional and composite excitations of antiferromagnetic quantum spin trimer chains

TL;DR

This study investigates the excitation spectrum of antiferromagnetic quantum spin trimer chains, revealing fractionalized excitations and a critical point where energy gaps close, with implications for experimental observation in neutron scattering.

Contribution

The paper provides a detailed analysis of the spectrum of $S=1/2$ antiferromagnetic Heisenberg trimer chains, highlighting the evolution of excitations and identifying a critical coupling ratio where gaps close.

Findings

Identification of doublons and quartons as high-energy excitations.

Observation of a gap closing at g ≈ 0.716.

Evolution of the spinon continuum with coupling ratio.

Abstract

Using quantum Monte Carlo, exact diagonalization and perturbation theory, we study the spectrum of the $S=1/2$ antiferromagnetic Heisenberg trimer chain by varying the ratio $g=J_2/J_1$ of the intertrimer and intratrimer coupling strengths. The doublet ground states of trimers form effective interacting $S=1/2$ degrees of freedom described by a Heisenberg chain. Therefore, the conventional two-spinon continuum of width $\propto J_1$ when $g=1$ evolves into to a similar continuum of width $\propto J_2$ when $g\to 0$. The intermediate-energy and high-energy modes are termed \emph{doublons} and \emph{quartons} which fractionalize with increasing $g$ to form the conventional spinon continuum. In particular, at $g \approx 0.716$, the gap between the low-energy spinon branch and the high-energy band with mixed doublons, quartons, and spinons closes. These features should be observable in inelastic neutron scattering experiments if a quasi-one-dimensional quantum magnet with the linear trimer structure and $J_2<J_1$ can be identified. Our results may open a window for exploring the high-energy fractional excitations.