Quantum Monte Carlo study of itinerant ferromagnetism

Until recently there existed little evidence in support of the stability of ferromagnetism in the Hubbard model at finite U and thermodynamically relevant electronic densities, except for very special circumstances. This has to do with the fact that itinerant ferromagnetism is a strong-coupling phenomenon whose investigation requires non-perturbative techniques. Here we report the results of extensive finite-temperature Quantum Monte Carlo calculations for the Hubbard model with and without direct exchange interaction F, obtained in the limit of infinite spatial dimensions. We show that itinerant ferromagnetism is indeed stable in this limit but depends in a subtle way on the lattice, i.e. on the structure of the non-interacting density of states (DOS), and the electron density. At half filling (n = 1) a finite exchange F > 0 is necessary to stabilize ferromagnetism. The critical value F_c(U) decreases linearly with U for small U (Hartree-Fock limit) and proportional to 1/U for large U (Heisenberg limit). For n < 1 ferromagnetism becomes stable even at F = 0 provided the non-interacting DOS is sufficiently high near the lower band edge. The stability regime of itinerant ferromagnetism is investigated systematically as a function of temperature T, density n, Hubbard interaction U, exchange interaction F and, in particular, of the spectral weight near the lower band edge.