Itinerant ferromagnetic phase of the Hubbard model

Using a quantum Monte Carlo technique, we provide strong evidence for the stability of a saturated ferromagnetic phase in the high-density regime of the two-dimensional infinite-$U$ Hubbard model. By decreasing the electron density, we observe a discontinuous transition to a paramagnetic phase, accompanied by a divergence of the susceptibility on the paramagnetic side. This behavior, resulting from a high degeneracy among different spin sectors, is consistent with an infinite-order phase transition. The remarkable stability of itinerant ferromagnetism renews the hope of describing this phenomenon within a purely kinetic mechanism and will facilitate the validation of experimental quantum simulators with cold atoms loaded in optical lattices.

Figure 1

Energy $E_f^0(\tau )=E_b^0-\partial {}_{\tau }\log {\mathcal{C}}_{\mathcal{A}}(\tau )$ as a function of the imaginary time $\tau$ for $L=50$ and $N=42$ electrons and different magnetizations. The dashed horizontal lines are FN energies, while the solid lines are the energies as obtained by fitting the imaginary-time correlations.

Figure 2

Ground-state magnetization of the infinite-$U$ Hubbard model on the square lattice. The shaded area represents a small region of uncertain attribution due to the effect of the residual Monte Carlo error.

Figure 3

Difference between the energy per site of different magnetizations and that of the saturated ferromagnet as a function of the density $n$. The cases with $L=200$ (squares) and 400 (circles) are reported; lines connecting points are a guide for the eye.