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

2026/07/22 by Yang Zhang, Cristian D. Batista
#cond-mat.str-el #cond-mat.supr-con

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Abstract

We study the single-hole infinite-U Hubbard model on the triangular lattice with nearest- and next-nearest-neighbor hoppings t₁ and t₂. A frustrating t₂ destabilizes Nagaoka ferromagnetism through a Lifshitz transition to a long-wavelength coplanar spiral at t_2,c/t₁=-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≃0.92 at the Lifshitz-shifted momentum K=-Q^*. 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.

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