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

Abstract

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 non-zero $U$, the honeycomb lattice is known to have a semi-metal phase at small $U$ and an antiferromagnetic one at large $U$. We investigate the phase transition at T=0 by studying the magnetic structure$and compressibility using quantum monte carlo simulations and by calculating the sublattice magnetization, uniform susceptibility, spin-wave and single hole ordered phase. Our results are consistent with a single continuous transition at$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(T)$, which changes from a two-peaked structure for$U>U_c$to a one-peaked structure for$U < U_c$. Furthermore, the$U$dependence of the low temperature coefficient of$C(T)$exhibits an anomaly at$U \approx U_c$.Comment: 11 pages, 19 figure