Z. Phys. B 103, 335–338 (1997) ZEITSCHRIFT F ¨ UR PHYSIK B c  Springer-Verlag 1997 Mott-Hubbard transition and antiferromagnetism on the honeycomb lattice L. M. Martelo ? , M. Dzierzawa, L. Siffert, D. Baeriswyl Institut de Physique Th´ eorique, Universit´ e de Fribourg, P´ erolles, CH-1700 Fribourg, Switzerland Abstract. The Hubbard model is investigated for a half- filled honeycomb lattice, using a variational method. Two trial wave functions are introduced, the Gutzwiller wave function, well suited for describing the “metallic” phase at small U and a complementary wave function for the insu- lating regime at large values of U . The comparison of the two variational ground states at the mean-field level yields a Mott transition at U c /t ≈ 5.3. In addition, a variational Monte Carlo calculation is performed in order to locate the instability of the “metallic” wave function with respect to an- tiferromagnetism. The critical value U m /t ≈ 3.7 obtained in this way is considered to be a lower bound for the true criti- cal point for antiferromagnetism, whereas there are good ar- guments that the mean-field value U c /t ≈ 5.3 represents an upper bound for the Mott transition. Therefore the “metal”- insulator transition for the honeycomb lattice may indeed be simultaneously driven by the antiferromagnetic instability and the Mott phenomenon. I. Introduction The metal-insulator transition produced by electron correla- tions, known as the Mott-Hubbard transition [1], is still not completely understood, despite of recent advances in the limit of large dimensions [2] and the development of new techniques for treating low-dimensional many-fermion mod- els [3]. The main reason for this slow progress is of course the difficulty of mastering the problem of strong correla- tions. In addition, the (pure) Mott-Hubbard transition is of- ten masked by an antiferromagnetic instability of the metallic phase. This is for instance the case for the Hubbard model on a hypercubic lattice: at half filling it has an antiferromag- netic ground state for any positive on-site repulsion U . At small U the antiferromagnetic ordering produces a gap at the Fermi energy [4], and with increasing U there is a smooth crossover to an antiferromagnetic Mott insulator. ? Present address: Department of Physics, University of ´ Evora, Apartado 94, P-7001 ´ Evora Codex, Portugal There exist ways for escaping the Slater (or spin-density wave) instability of the metallic phase, for instance frustra- tion introduced by the geometry of the lattice or the addi- tion of hopping between next-nearest neighbors, reducing the nesting of the Fermi surface. Another way out is of- fered by specific lattice symmetries which entail a vanishing density of states at the Fermi energy and therefore strongly reduce the tendency towards the opening of a spin-density wave gap. An important example is the honeycomb lattice considered in this paper. For the sake of completeness we mention that also in cases where the Slater instability is not suppressed at zero temperature the Mott-Hubbard transition can survive, namely at temperatures above the transition to a paramag- netic phase [2]. This happens because the energy scale for the magnetic instability is typically smaller than that for the Mott transition. It is worth mentioning that besides the transi- tion as a function of U there is also a transition as a function of band filling. In fact, the understanding of a doped Mott insulator has become one of the key issues in the theory of high-temperature superconductors [5]. The starting point for our investigations is the Hubbard model [6], which is defined as ˆ H = ˆ T + U ˆ D (1) where ˆ T = -t ∑ <ij>,σ ˆ c † iσ ˆ c jσ transfers electrons between nearest neighbor sites of the lattice and ˆ D = ∑ i ˆ n i↑ ˆ n i↓ mea- sures the number of doubly occupied sites. The operators ˆ c † iσ (ˆ c iσ ) create (annihilate) electrons on site i with spin pro- jection σ and ˆ n iσ =ˆ c † iσ ˆ c iσ . Throughout this paper we limit ourselves to the case of a half filled band in the limit of zero temperature. II. Variational approach Our aim is to approach the Mott-Hubbard transition from the metallic and insulating sides using two different variational wave functions. In the small U region, where the system is expected to be metallic, we use the Gutzwiller wave function [7] ψ G = e -η ˆ D ψ 0 . (2)