Ground-state and finite-temperature signatures of quantum phase transitions in the half-filled Hubbard model on a honeycomb lattice

We investigate ground state and finite temperature properties of the half-filled Hubbard model on a honeycomb lattice using quantum Monte Carlo and series expansion techniques. Unlike the square lattice, for which magnetic order exists at $T=0$ for any nonzero $U$, the honeycomb lattice is known to have a semimetal phase at small $U$ and an antiferromagnetic one at large $U$. We investigate the phase transition at $T=0$ by studying the magnetic structure factor and compressibility using quantum Monte Carlo simulations and by calculating the sublattice magnetization, uniform susceptibility, spinwave, and single hole dispersion using series expansions around the ordered phase. Our results are consistent with a single continuous transition at $U_c∕t$ in the range 4–5. Finite-temperature signatures of this phase transition are seen in the behavior of the specific heat, $C\left(T\right)$, which changes from a two-peaked structure for $U>U_c$ to a one-peaked structure for $U<U_c$. Furthermore, the $U$ dependence of the low temperature coefficient of $C\left(T\right)$ exhibits an anomaly at $U\approx U_c$.