Phase diagram of the Hubbard model on a honeycomb lattice: A cluster slave-spin study

The cluster slave-spin method is implemented to research the ground state properties of honeycomb lattice Hubbard model with doping $\delta$ and coupling $U$ being its parameters. At half-filling, a single direct continuous phase transition between semi-metal antiferromagnetic (AFM) insulator found at $U_{\text{AFM}}=2.43t$ that in Gross-Neveu-Yukawa universality class, where relation staggered magnetization $M$ AFM energy gap $\Delta_{\text{AFM}}$ established as $M \propto \Delta_{\text{AFM}}$, compared \Delta_{\text{AFM}} ( \ln{\Delta_{\text{AFM}}})^2$ square case. A first-order underlying paramagnetic (PM) Mott corroborated $U_{\text{Mott}}=8.36t$, which responsible for broad crossover around $U_{c} = 5.4t$ weak- strong-coupling regimes increases $\delta$, contrast In doped system, compressibility $\kappa$ near van Hove singularity $\delta=1/4$ suppressed substantially by interaction before occurs, whereas Dirac points very close noninteracting one, indicating cone structure dispersion rather robust. An overall diagram $U$-$\delta$ plane presented, consisting four regimes: $\delta=0$ $U> U_{\text{AFM}}$, metal $\kappa>0$ or $\kappa<0$, PM semi-metal, $\kappa<0$ only exists an extremely small area boundary state.