Loop-Cluster Simulation of the $t$-$J$ Model on the Honeycomb Lattice

Inspired by the lattice structure of the unhydrated variant of the superconducting material Na${}_x$CoO${}_2\cdot$yH${}_2$O at $x=1\mathrm{/}3$, 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 ${\tilde{\mathcal{M}}}_s=0.2688(3)$, the spin stiffness ${\rho }_s=0.102(2)J$, the spin wave velocity $c=1.297(16)Ja$, and the kinetic mass $M^{\mathrm{\prime }}$ of a hole are obtained by fitting the numerical Monte Carlo data to the effective theory predictions.