Solving the dynamical mean-field theory at very low temperatures using the Lanczos exact diagonalization

We present an efficient method to solve the impurity Hamiltonians involved in dynamical mean-field theory at low but finite temperature based on the extension of the Lanczos algorithm from ground state properties alone to excited states. We test the approach on the prototypical Hubbard model and find extremely accurate results from $T=0$ up to relatively high temperatures up to the scale of the critical temperature for the Mott transition. The algorithm substantially decreases the computational effort involved in finite temperature calculations.