Fractional and composite excitations of antiferromagnetic quantum spin trimer chains

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.

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