Breakdown of the Nagaoka phase in the two-dimensional (formula presented) model

In the limit of weak exchange J at low hole concentration (formula presented) the ground state of the two-dimensional (formula presented) model is believed to be ferromagnetic. We study the leading instability of this Nagaoka state, which emerges with increasing J. Both exact diagonalization of small clusters, and a semiclassical analytical calculation of larger systems show that above a certain critical value of the exchange, (formula presented) Nagaoka’s state is unstable to phase separation. In a finite-size system a bubble of antiferromagnetic Mott insulator appears in the ground state above this threshold. The size of this bubble depends on (formula presented) and scales as a power of the system size N.