Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2607.20726

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

Yang Zhang, Cristian D. Batista

Published Jul 22, 2026• 0 citations
arXivHTMLPDF

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 $Z\simeq0.92$ at the Lifshitz-shifted momentum $\mathbf{K}=-\mathbf{Q}^*$. 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.

DOI
10.48550/arxiv.2607.20726

Related papers

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

Darren Pereira, Erich J. Mueller

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 transition, finding the exact location of the spin-spiral instability.

arXiv:2510.05226•Physical review. B./Physical review. B•Apr 1, 2026•0 citations

Instability of Nagaoka state and quantum phase transition via kinetic frustration control

P. A. Sharma, Yang Peng, D. N. Sheng +2 more

We investigate the Nagaoka-Thouless ferromagnetic instability in the strongly interacting t − t ′ Hubbard model by continuously breaking particle-hole symmetry on a tunable square-triangular lattice geometry. We use an analytic approach to show that the fully spin-polarized state becomes unstable to a metastable spin polaron when the kinetic frustration t ′ / t exceeds a critical, dimension-dependent value. Large-scale density matrix renormalization group simulations reveal a quantum phase transition from the Nagaoka ferromagnet to a spiral spin-density wave, which evolves continuously into the Haerter-Shastry antiferromagnet in the large-frustration limit. Remarkably, this transition remains robust at low but finite hole density, making it accessible in cold-atom and moiré Hubbard platforms under strong interactions. A variational analysis further captures the instability mechanism at finite hole density via frustration-induced magnon band deformation.

arXiv:2508.08410•Physical Review Research•Mar 24, 2026•5 citations

Evolution of Nagaoka phase with kinetic energy frustrating hopping

Franco T. Lisandrini, Barbara Bravo, A. E. Trumper +2 more

We investigate, using the density-matrix renormalization group, the evolution of the Nagaoka state with ${t}^{\ensuremath{'}}$ hopping that frustrates the hole kinetic energy in the $U=\ensuremath{\infty}$ Hubbard model on the square and anisotropic triangular lattices. We find that the Nagaoka ferromagnet survives up to a rather small ${t}_{c}^{\ensuremath{'}}/t\ensuremath{\sim}0.2.$ At this critical value, there is a transition to an antiferromagnetic phase that depends on the lattice: a $\mathbf{Q}=(Q,0)$ spiral order, which continuously evolves with ${t}^{\ensuremath{'}}$, for the triangular lattice and the usual $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$ N\'eel order for the square lattice. Remarkably, the local magnetization takes its classical value for all considered ${t}^{\ensuremath{'}}$ (${t}^{\ensuremath{'}}/t\ensuremath{\le}1$). Our results show that the recently found classical kinetic antiferromagnetism, a perfect counterpart of Nagaoka ferromagnetism, is a generic phenomenon in these kinetically frustrated electronic systems.

arXiv:1702.00417•Physical review. B./Physical review. B•May 2, 2017•14 citations

Magnon-Mediated Superconductivity in the Infinite-$U$ Triangular Lattice

Hantian Zhu, Yixin Zhang, Shang-Shun Zhang +2 more

We demonstrate that the infinite-$U$ triangular-lattice Hubbard model supports a superconducting state built from tightly bound Cooper pairs composed of two holes and one magnon ($2h1m$). Building on the seminal prediction of repulsively bound $2h1m$ states, we show that next-nearest-neighbor hopping $t_{2}$ coherently mixes symmetry-related configurations, stabilizing an $s$-wave bound state with substantial binding energy and a light effective mass. Large-scale DMRG calculations at finite doping identify a magnetization plateau corresponding to a gas of such bound states and quasi--long--range superconducting order with power-law $2h1m$ pair correlations. Our results establish a magnon-mediated superconducting mechanism driven by kinetic frustration, with immediate detectable signatures for moiré Hubbard materials and ultracold-atom simulators.

arXiv:2602.06231•Feb 5, 2026•0 citations

Holes in the infinite-UHubbard model: Instability of the Nagaoka state

Yan Yan Fang, Andrei E. Ruckenstein, Elbio R. Dagotto +1 more

The solution of a three-body Schr\"odinger equation (for two holes and a spin flip) shows that in the U=\ensuremath{\infty} Hubbard model the saturated ferromagnetic state with two holes is unstable (in a finite volume and for periodic boundary conditions). The ground state carries a finite momentum, and becomes degenerate with the Nagaoka state in the thermodynamic limit. This is in agreement with exact diagonalization results for small lattices where, in addition, we find that the true two-hole ground state is a singlet. As a result, our notions of ferromagnetism in the Hubbard model might need revision.

Physical review. B, Condensed matter•Oct 1, 1989•79 citations

Hole and electron dynamics in a triangular-lattice antiferromagnet: Interplay of frustration and spin fluctuations

Pooja Srivastava, Avinash Singh

Single-particle dynamics in the 120\ifmmode^\circ\else\textdegree\fi{} ordered antiferromagnetic state of the triangular-lattice Hubbard model is studied using a physically transparent fluctuation approach in terms of multiple magnon emission and absorption processes within the noncrossing approximation. Hole and electron spectral features are evaluated at intermediate $U$, and analyzed in terms of a competition between the frustration-induced direct hopping and the virtual hopping. Finite $U$-induced competing interactions and frustration effects contributing through the magnon dispersion are also discussed. Finite contribution to self-energy correction from long-wavelength (Goldstone) modes, together with the high density of electron scattering states in the narrow, sharp peak in the upper band, result in strong fermion-magnon scattering leading to pronounced incoherent behavior in the electron dynamics. The fluctuation-induced first-order metal-insulator transition due to vanishing band gap is also discussed.

arXiv:cond-mat/0506488•Physical Review B•Dec 7, 2005•6 citations
We study the single-hole infinite-UUU Hubbard model on the triangular lattice with nearest- and next-nearest-neighbor hoppings t1t_1t1​ and t2t_2t2​. A frustrating t2t_2t2​ destabilizes Nagaoka ferromagnetism through a Lifshitz transition to a long-wavelength coplanar spiral at t2,c/t1=−0.182t_{2,c}/t_1=-0.182t2,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≃0.92Z\simeq0.92Z≃0.92 at the Lifshitz-shifted momentum K=−Q∗\mathbf{K}=-\mathbf{Q}^*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.
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 transition, finding the exact location of the spin-spiral instability.
We investigate the Nagaoka-Thouless ferromagnetic instability in the strongly interacting t − t ′ Hubbard model by continuously breaking particle-hole symmetry on a tunable square-triangular lattice geometry. We use an analytic approach to show that the fully spin-polarized state becomes unstable to a metastable spin polaron when the kinetic frustration t ′ / t exceeds a critical, dimension-dependent value. Large-scale density matrix renormalization group simulations reveal a quantum phase transition from the Nagaoka ferromagnet to a spiral spin-density wave, which evolves continuously into the Haerter-Shastry antiferromagnet in the large-frustration limit. Remarkably, this transition remains robust at low but finite hole density, making it accessible in cold-atom and moiré Hubbard platforms under strong interactions. A variational analysis further captures the instability mechanism at finite hole density via frustration-induced magnon band deformation.
We investigate, using the density-matrix renormalization group, the evolution of the Nagaoka state with ${t}^{\ensuremath{'}}$ hopping that frustrates the hole kinetic energy in the $U=\ensuremath{\infty}$ Hubbard model on the square and anisotropic triangular lattices. We find that the Nagaoka ferromagnet survives up to a rather small ${t}_{c}^{\ensuremath{'}}/t\ensuremath{\sim}0.2.$ At this critical value, there is a transition to an antiferromagnetic phase that depends on the lattice: a Q=(Q,0)\mathbf{Q}=(Q,0)Q=(Q,0) spiral order, which continuously evolves with ${t}^{\ensuremath{'}}$, for the triangular lattice and the usual $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$ N\'eel order for the square lattice. Remarkably, the local magnetization takes its classical value for all considered ${t}^{\ensuremath{'}}$ (${t}^{\ensuremath{'}}/t\ensuremath{\le}1$). Our results show that the recently found classical kinetic antiferromagnetism, a perfect counterpart of Nagaoka ferromagnetism, is a generic phenomenon in these kinetically frustrated electronic systems.
Magnon-Mediated Superconductivity in the Infinite-UUU Triangular Lattice
We demonstrate that the infinite-UUU triangular-lattice Hubbard model supports a superconducting state built from tightly bound Cooper pairs composed of two holes and one magnon (2h1m2h1m2h1m). Building on the seminal prediction of repulsively bound 2h1m2h1m2h1m states, we show that next-nearest-neighbor hopping t2t_{2}t2​ coherently mixes symmetry-related configurations, stabilizing an sss-wave bound state with substantial binding energy and a light effective mass. Large-scale DMRG calculations at finite doping identify a magnetization plateau corresponding to a gas of such bound states and quasi--long--range superconducting order with power-law 2h1m2h1m2h1m pair correlations. Our results establish a magnon-mediated superconducting mechanism driven by kinetic frustration, with immediate detectable signatures for moiré Hubbard materials and ultracold-atom simulators.
The solution of a three-body Schr\"odinger equation (for two holes and a spin flip) shows that in the U=\ensuremath{\infty} Hubbard model the saturated ferromagnetic state with two holes is unstable (in a finite volume and for periodic boundary conditions). The ground state carries a finite momentum, and becomes degenerate with the Nagaoka state in the thermodynamic limit. This is in agreement with exact diagonalization results for small lattices where, in addition, we find that the true two-hole ground state is a singlet. As a result, our notions of ferromagnetism in the Hubbard model might need revision.
Single-particle dynamics in the 120\ifmmode^\circ\else\textdegree\fi{} ordered antiferromagnetic state of the triangular-lattice Hubbard model is studied using a physically transparent fluctuation approach in terms of multiple magnon emission and absorption processes within the noncrossing approximation. Hole and electron spectral features are evaluated at intermediate UUU, and analyzed in terms of a competition between the frustration-induced direct hopping and the virtual hopping. Finite UUU-induced competing interactions and frustration effects contributing through the magnon dispersion are also discussed. Finite contribution to self-energy correction from long-wavelength (Goldstone) modes, together with the high density of electron scattering states in the narrow, sharp peak in the upper band, result in strong fermion-magnon scattering leading to pronounced incoherent behavior in the electron dynamics. The fluctuation-induced first-order metal-insulator transition due to vanishing band gap is also discussed.