https://doi.org/10.1140/epjb/s10051-026-01179-2
Research - Condensed Matter
Spin-wave excitations of the triangular-lattice Hubbard model: strong-coupling limit and finite-U effects
Department of Physics, Amity Institute of Applied Sciences, Amity University Kolkata, Major Arterial Road, Action Area II, 700135, Kolkata, West Bengal, India
a
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Received:
14
February
2026
Accepted:
30
April
2026
Published online:
21
May
2026
Abstract
We investigate transverse spin-wave excitations of the half-filled Hubbard model on a two-dimensional triangular lattice, focusing on both the strong-coupling and finite-U regimes. Starting from a spiral Hartree–Fock description of the 
non-collinear antiferromagnetic ground state, we evaluate the dynamical transverse spin susceptibility within the random phase approximation (RPA), building on established itinerant-electron formulations. In the strong-coupling limit 
, we obtain an analytic closed-form expression for the magnon dispersion and demonstrate explicitly that it reduces identically to the linear spin-wave theory result of the nearest-neighbor Heisenberg antiferromagnet with exchange 
, thereby recovering the correct Goldstone modes and long-wavelength behavior. Retaining subleading terms in the strong-coupling expansion of the bare particle–hole propagator to order 
, we derive an explicit analytic expression for the finite-U renormalization of the spin-wave spectrum. The resulting magnon energy acquires a momentum-dependent multiplicative correction proportional to 
, leading to a systematic softening relative to the Heisenberg limit while preserving spin-rotational symmetry. From the long-wavelength expansion, we obtain a closed-form expression for the spin stiffness and show that it is reduced according to ![Mathematical equation: $$\rho (U)=\rho _0[1-(243/8)(t^2/U^2)]$$](/articles/epjb/abs/2026/05/10051_2026_Article_1179/10051_2026_Article_1179_tex_eq6.png)
, implying a collapse of the stiffness at 
within the present RPA-level treatment. Our results provide a transparent dynamical demonstration of the strong-coupling correspondence between itinerant and localized descriptions of a frustrated non-collinear antiferromagnet, and establish a controlled analytic framework for incorporating finite-U itinerant effects in triangular-lattice Hubbard systems.
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
