Abstract. The antiferromagnetic transition of the two dimensional Hubbard model is analyzed by comparing the available exact, numerical and mean field results. It is argued that all data is compatible with the opening of a mean field gap in a Fermi liquid of spin polarons, the so called Slater type of transition. In particular, this hypothesis explains the unusual dispersion relation of the quasiparticle bands near the transition. PACS. 71.10.Fd Lattice fermion models (Hubbard model, etc.) – 71.30.+h Metal-insulator transitions and other electronic transitions The nature of the insulating phase of the Hubbard model has attracted a great deal of attention. A clarification of the universality class of the transition will greatly help in understanding the nature of the “metallic ”, gapless phase away from half doping. A detailed discussion of the issue can be found in [1]. Opposing viewpoints on the problem are presented in [2,3]. An appealing approach is the scaling analysis discussed in [1]. It is assumed that
Charge dynamics of the two-dimensional Hubbard model is investigated. Lancz
o¨s-diagonalization results for the optical conductivity and the Drude weight of this model are presented. Near the Mott transition, large incoherence below the upper-Hubbard band is obtained together with a remarkably suppressed Drude weight in two dimensions while the clearly coherent character is shown in one dimension. The two-dimensional results are consistent with previous results from quantum Monte Carlo calculations indicating that the Mott transition in this two-dimensional model belongs to the universality class characterized by the dynamical exponent of
z=4.
Recent quantum-gas microscopy of ultracold atoms and scanning tunneling microscopy of the cuprates reveal new detailed information about doped Mott antiferromagnets, which can be compared with calculations. Using cellular dynamical mean-field theory, we map out the antiferromagnetic (AF) phase of the two-dimensional Hubbard model as a function of interaction strength
U, hole doping $\ensuremath{\delta}$, and temperature
T. The N\'eel phase boundary is nonmonotonic as a function of
U and $\ensuremath{\delta}$. Frustration induced by second-neighbor hopping reduces N\'eel order more effectively at small
U. The doped AF is stabilized at large
U by kinetic energy and at small
U by potential energy. The transition between the AF insulator and the doped metallic AF is continuous. At large
U, we find in-gap states similar to those observed in scanning tunneling microscopy. We predict that, contrary to the Hubbard bands, these states are only slightly spin polarized.