Dynamical mean-field theory calculation with the dynamical density-matrix renormalization group

Abstract

We study the Hubbard model at half band-filling on a Bethe lattice with infinite coordination number at zero temperature. We use the dynamical mean-field theory (DMFT) mapping to a single-impurity Anderson model with a bath whose properties have to be determined self-consistently. For a controlled and systematic implementation of the self-consistency scheme we use the fixed-energy approach to the DMFT. Using the dynamical density–matrix renormalization group method (DDMRG) we calculate the density of states (DOS) with a resolution ranging from 3% of the bare bandwidth W = 4 t at high energies to 0.01% for the quasi-particle peak. The DDMRG resolution and accuracy for the DOS is superior to those obtained with other numerical methods in previous DMFT investigations. We find that the critical couplings are U c , 1 / t = 4.45 ± 0.05 and U c , 2 / t = 6.1 ± 0.1 . Our calculation indicate the existence of two metallic solutions below U = U c , 1 .