Exact Nagaoka-to-spiral transition in the doped infinite-U triangular lattice

Abstract

We study the single-hole infinite-$U$ Hubbard model on the triangular lattice with nearest- and next-nearest-neighbor hoppings $t_1$ and $t_2$. A frustrating $t_2$ destabilizes Nagaoka ferromagnetism through a Lifshitz transition to a long-wavelength coplanar spiral at $t_{2,c}/t_1=-0.182$. We determine the critical point analytically by reducing the many-body problem to an effective two-body hole--magnon scattering problem in which the hard-core hole--magnon constraint is treated exactly. Numerical calculations confirm the spiral ground state and reveal a coherent spin polaron with quasiparticle weight $Z\simeq 0.92$ at the Lifshitz-shifted momentum $\mathbf{K}=-{\mathbf{Q}}^{\ast }$. These results establish the first quantum instability of the triangular-lattice Nagaoka ferromagnet and provide the magnetic baseline for magnon-mediated pairing at finite doping.

4+11 pages, 3+3 figures