Metal-insulator transition in the two-dimensional Hubbard model: Dual fermion approach with Lanczos exact diagonalization

Abstract

In this study the metal-insulator transition in the square-lattice Hubbard model at half-filling is revisited in relation to the DOS and spectral functions by means of the ladder dual fermion approximation (LDFA). For this purpose, a new expression of the two-body Green's function in the form of resolvents is proposed, which provides tractable and efficient means to calculate the local vertex function with the Lanczos exact diagonalization (ED) method. This makes it possible to use the Lanczos ED method as a solver of the effective impurity Anderson model for LDFA, opening up the way to access low temperatures for these perturbative extensions of the dynamical mean field theory and to obtain accurate DOS and spectral functions on the real frequency axis by a new variant of the maximum entropy method. It is found that for $U\le 3.5t$, as temperature decreases, the pseudogap formation due to antiferromagnetic correlations in the quasiparticle peak of the spectral function occurs at the X point $[k=(\pi,0)]$, spreads through the Fermi surface and ends at the M$_2$ point $[k=(\pi/2,\pi/2)]$. The almost simultaneous creation of the pseudogap and the loss of the Fermi liquid feature is consistent with that expected in the Slater regime. Although the pseudogap still appears in the quasi-particle-like single peak for $U\ge 4.0t$, the Fermi-liquid feature is partially lost on the Fermi surface already at higher temperatures as expected in the Mott-Heisenberg regime, in which local spins are preformed at high temperatures. A sharp crossover from a pseudogap phase to a Mott insulator at finite $U^{*} \approx 4.7t$ is found to occur below the temperature of the pseudogap formation similar to a previous study with the non-linear $\sigma$ model approach.