Finite-temperature numerical renormalization group study of the Mott transition

Wilson's numerical renormalization group method for the calculation of dynamic properties of impurity models is generalized to investigate the effective impurity model of the dynamical mean-field theory at finite temperatures. We calculate the spectral function and self-energy for the Hubbard model on a Bethe lattice with infinite coordination number directly on the real-frequency axis and investigate the phase diagram for the Mott-Hubbard metal-insulator transition. While for T<Tc≈0.02W $(W:$ bandwidth) we find hysteresis with first-order transitions both at Uc1 (defining the insulator to metal transition) and at Uc2 (defining the metal to insulator transition), at T>Tc there is a smooth crossover from metalliclike to insulatinglike solutions.