Phase diagram of the Hubbard model on a square lattice: A cluster slave-spin study

Abstract

The cluster slave-spin method is employed to investigate systematically the ground state properties of the Hubbard model on a square lattice with doping δ and coupling strength U being its parameters. At half-filling, a relation between the staggered magnetization M and the antiferromagnetic (AFM) gap ∆AFM is established in the small U limit to compare with that from the Hartree-Fock theory, and a first-order metal-insulator Mott transition in the paramagnetic state is substantiated, which is characterized by discontinuities and hystereses at UMott = 10t. The interaction Uc for the crossover in the AFM state, separating the weakand strong-coupling regimes, is found to remain almost unchanged with large dopings, and smaller than UMott at half-filling because of long range AFM correlations. Finally, an overall phase diagram in the U -δ plane is presented, which is composed of four regimes: the AFM insulator at half-filling, the AFM metal with the compressibility κ > 0 or κ < 0, and the paramagnetic metal, as well as three phase transitions: (i) From the AFM metal to the paramagnetic metal, (ii) between the AFM metal phases with positive and negative κ, and (iii) separating the AFM insulating phase at δ = 0 from the AFM metal phase for δ > 0.