Loop-cluster simulation of the zero- and one-hole sectors of the t-J model on the honeycomb lattice

Inspired by the unhydrated variant of the superconducting material Na _xCoO₂·yH₂O at x=1/3, we study the t-J model on a honeycomb lattice by using an efficient loop-cluster algorithm. The low-energy physics of the undoped system and of the single-hole sector is described by a systematic low-energy effective field theory. The staggered magnetization per spin M̃_s=0.2688 (3), the spin stiffness ρ_s=0.102 (2) J, the spin-wave velocity c=1.297 (16) Ja, and the kinetic mass M′ of a hole are obtained by fitting the numerical Monte Carlo data to the effective field theory predictions.