Spin-spiral instability of the Nagaoka ferromagnet in the crossover between square and triangular lattices

Abstract: We study the hard-core Fermi-Hubbard model in the crossover between square and triangular lattices near half-filling. As was recognized by Nagaoka in the 1960s, on the square lattice the presence of a single hole leads to ferromagnetic spin ordering. On the triangular lattice, geometric frustration instead leads to a spin-singlet ground state, which can be associated with a 120-degree spiral order. On lattices which interpolate between square and triangular, there is a phase transition at which the ferromagnetic order becomes unstable to a spin spiral. We model this instability, finding the exact critical point.