Coexistence of solutions in dynamical mean-field theory of the Mott transition

In this paper, I discuss the finite-temperature metal-insulator transition of the paramagnetic Hubbard model within dynamical mean-field theory. I show that coexisting solutions, the hallmark of such a transition, can be obtained in a consistent way both from quantum Monte Carlo (QMC) simulations and from the exact diagonalization method. I pay special attention to discretization errors within the QMC method. These errors explain why it is difficult to obtain the solutions from the QMC method close to the boundaries of the coexistence region.