Spinons and Spin-Charge Separation at the Deconfined Quantum Critical Point

Using quantum Monte Carlo and numerical analytic continuation methods, we study the dynamic spin structure factor and the single-hole spectral function of a two-dimensional quantum magnet ($J$-$Q$ model) at its quantum phase transition separating N\'eel antiferromagnetic and spontaneously dimerized ground states. At this putative deconfined quantum-critical point, we find a broad continuum of spinon excitations that can be accounted for by the fermionic $\pi$-flux state; a known mean-field model for deconfined quantum criticality. We find that the best description of the two-spinon continuum is with a version of the model with a $2\times 2$ unit cell, reflecting non-trivial mutual statistics of spinons and anti-spinons. The single-hole spectral function can be described by the same spinon dispersion relation and an independently propagating holon. Thus, the system exhibits spin-charge separation and will likely evolve into an extended holon metal phase at finite doping.