Fermionic SK-models with Hubbard interaction: Magnetism and electronic structure

TL;DR

This paper provides an exact analysis of fermionic SK-models with Hubbard interaction, revealing detailed phase diagrams, density of states behavior, and transitions between insulating phases, with implications for metal-insulator transitions.

Contribution

It introduces an exact solution method for fermionic SK-models with Hubbard interaction, including RSB effects up to four steps, and characterizes phase transitions and density of states near the Fermi level.

Findings

Density of states near Fermi level follows (E)=const |E-E_F|

Identifies a half-filling transition with scaling behavior

Predicts a transition between insulating phases with different pseudogaps

Abstract

Models with range-free frustrated Ising spin- and Hubbard interaction are treated exactly by means of the discrete time slicing method. Critical and tricritical points, correlations, and the fermion propagator, are derived as a function of temperature T, chemical potential \mu, Hubbard coupling U, and spin glass energy J. The phase diagram is obtained. Replica symmetry breaking (RSB)-effects are evaluated up to four-step order (4RSB). The use of exact relations together with the 4RSB-solutions allow to model exact solutions by interpolation. For T=0, our numerical results provide strong evidence that the exact density of states in the spin glass pseudogap regime obeys \rho(E)=const |E-E_F| for energies close to the Fermi level. Rapid convergence of \rho'(E_F) under increasing order of RSB is observed. The leading term resembles the Efros-Shklovskii Coulomb pseudogap of localized disordered fermionic systems in 2D. Beyond half filling we obtain a quadratic dependence of the fermion filling factor on the chemical potential. We find a half filling transition between a phase for U>\mu, where the Fermi level lies inside the Hubbard gap, into a phase where \mu(>U) is located at the center of the upper spin glass pseudogap (SG-gap). For \mu>U the Hubbard gap combines with the lower one of two SG-gaps (phase I), while for \mu<U it joins the sole SG-gap of the half-filling regime (phase II). We predict scaling behaviour at the continuous half filling transition. Implications of the half-filling transition between the deeper insulating phase II and phase I for delocalization due to hopping processes in itinerant model extensions are discussed and metal-insulator transition scenarios described.