Semi-Metal-Insulator Transition of the Hubbard Model in the Honeycomb Lattice

Abstract

Using quantum Monte Carlo and finite-size scaling for the Hubbard model, we find evidence of a zero-temperature transition between the nonmagnetic semi-metal and an antiferromagnetic insulator in the 2D honeycomb lattice for a nontrivial value of U/t = 4.5 ± 0.5. The corresponding transition in Hartree-Fock mean field is at U/t = 2.23, which indicates the importance of quantum fluctuations. This represents the first example of Mott-Hubbard transition in a 2D bipartite lattice. Similar transitions are predicted for special lattices in higher dimensions, in particular for the 3D diamond lattice.