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:1702.00417 · Physical review. B./Physical review. B

Evolution of Nagaoka phase with kinetic energy frustrating hopping

Franco T. Lisandrini, Barbara Bravo, A. E. Trumper, L. O. Manuel, C. J. Gazza

Published May 2, 2017• 14 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.95.195103

Related papers

Classical Antiferromagnetism in Kinetically Frustrated Electronic Models

Cintia N. Sposetti, Barbara Bravo, A. E. Trumper +2 more

We study, by means of the density matrix renormalization group, the infinite U Hubbard model--with one hole doped away from half filling--in triangular and square lattices with frustrated hoppings, which invalidate Nagaoka's theorem. We find that these kinetically frustrated models have antiferromagnetic ground states with classical local magnetization in the thermodynamic limit. We identify the mechanism of this kinetic antiferromagnetism with the release of the kinetic energy frustration, as the hole moves in the established antiferromagnetic background. This release can occur in two different ways: by a nontrivial spin Berry phase acquired by the hole, or by the effective vanishing of the hopping amplitude along the frustrating loops.

arXiv:1312.6672•Physical Review Letters•May 9, 2014•37 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

Finite-temperature kinetic ferromagnetism in the square-lattice Hubbard model

Robert C. Newby, Ehsan Khatami

While the exact phase diagram of the Fermi-Hubbard model remains poorly understood despite decades of progress, nearly 60 years ago Nagaoka proved that a single dopant in an otherwise half-filled Hubbard system can bring about ferromagnetism through kinetic means. The phenomenon was recently observed with ultracold atoms in triangular optical lattices. Here, we explore the kinetic ferromagnetism within the square lattice Hubbard model and its strong-coupling counterpart, the $t\ensuremath{-}J$ model, at finite temperatures in the thermodynamic limit via numerical linked-cluster expansions. We find evidence of ferromagnetic Nagaoka polarons at dopings up to $\ensuremath{\sim}30%$ away from half filling for a variety of interaction strengths and at temperatures as low as 0.2 of the hopping energy. We map out the boundaries of this phase through analyzing various correlation functions.

arXiv:2502.07252•Physical review. B./Physical review. B•Jun 6, 2025•6 citations

High-temperature kinetic magnetism in triangular lattices

Ivan Morera, Márton Kanász-Nagy, Tomasz Smoleński +3 more

We study kinetic magnetism for the Fermi-Hubbard models in triangular type lattices, including a zigzag ladder, four- and six-legged triangular cylinders and a full two-dimensional triangular lattice. We focus on the regime of strong interactions, $U\gg t$ and filling factors around one electron per site. For temperatures well above the hopping strength, the Curie-Weiss form of the magnetic susceptibility suggests effective antiferromagnetic correlations for systems that are hole doped with respect to $ν=1$, and ferromagnetic correlations for systems with electron dopings. We show that these correlations arise from magnetic polaron dressing of charge carrier propagating in a spin incoherent Mott insulator. Effective interactions corresponding to these correlations can strongly exceed the magnetic super-exchange energy. In the case of hole doping, antiferromagnetic polarons originate from kinetic frustration of individual holes in a triangular lattice. In the case of electron doping, Nagaoka type ferromagnetic correlations are induced by propagating doublons. These results provide a theoretical explanation of recent experimental results in moire TMDC materials. To understand many-body states arising from antiferromagentic polarons at low temperatures, we study hole doped systems in finite magnetic fields. At low dopings and intermediate magnetic fields we find a magnetic polaron phase, separated from the fully polarized state by a metamagnetic transition. With decreasing magnetic field the system shows a tendency to phase separate, with hole rich regions forming antiferromagnetic spinbags. We demonstrate that direct observations of magnetic polarons in triangular lattices can be achieved in experiments with ultracold atoms, which allow measurements of three point hole-spin-spin correlations.

arXiv:2209.05398•Sep 12, 2022•6 citations

Nagaoka ferromagnetism in doped Hubbard models in optical lattices

Rhine Samajdar, R. N. Bhatt

Finding ferromagnetic ground states of the Hubbard model, which usually features antiferromagnetic spin correlations, has been an outstanding challenge since Nagaoka's celebrated (but experimentally unrealistic) proposal in 1966. Here, the authors show how such elusive itinerant ferromagnetism can be enhanced by kinetic frustration or occupation-dependent hoppings and demonstrate the relevance of these mechanisms to recent optical-lattice experiments.

arXiv:2305.05683•Physical Review A•Aug 22, 2024•14 citations

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
We investigate, using the density-matrix renormalization group, the evolution of the Nagaoka state with t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′ hopping that frustrates the hole kinetic energy in the U=\ensuremath∞U=\ensuremath{\infty}U=\ensuremath∞ Hubbard model on the square and anisotropic triangular lattices. We find that the Nagaoka ferromagnet survives up to a rather small tc\ensuremath′/t\ensuremath∼0.2.{t}_{c}^{\ensuremath{'}}/t\ensuremath{\sim}0.2.tc\ensuremath′​/t\ensuremath∼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′{t}^{\ensuremath{'}}t\ensuremath′, for the triangular lattice and the usual Q=(\ensuremathπ,\ensuremathπ)\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})Q=(\ensuremathπ,\ensuremathπ) N'eel order for the square lattice. Remarkably, the local magnetization takes its classical value for all considered t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′ (t\ensuremath′/t\ensuremath≤1{t}^{\ensuremath{'}}/t\ensuremath{\le}1t\ensuremath′/t\ensuremath≤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.
We study, by means of the density matrix renormalization group, the infinite U Hubbard model--with one hole doped away from half filling--in triangular and square lattices with frustrated hoppings, which invalidate Nagaoka's theorem. We find that these kinetically frustrated models have antiferromagnetic ground states with classical local magnetization in the thermodynamic limit. We identify the mechanism of this kinetic antiferromagnetism with the release of the kinetic energy frustration, as the hole moves in the established antiferromagnetic background. This release can occur in two different ways: by a nontrivial spin Berry phase acquired by the hole, or by the effective vanishing of the hopping amplitude along the frustrating loops.
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.
While the exact phase diagram of the Fermi-Hubbard model remains poorly understood despite decades of progress, nearly 60 years ago Nagaoka proved that a single dopant in an otherwise half-filled Hubbard system can bring about ferromagnetism through kinetic means. The phenomenon was recently observed with ultracold atoms in triangular optical lattices. Here, we explore the kinetic ferromagnetism within the square lattice Hubbard model and its strong-coupling counterpart, the $t\ensuremath{-}J$ model, at finite temperatures in the thermodynamic limit via numerical linked-cluster expansions. We find evidence of ferromagnetic Nagaoka polarons at dopings up to $\ensuremath{\sim}30%$ away from half filling for a variety of interaction strengths and at temperatures as low as 0.2 of the hopping energy. We map out the boundaries of this phase through analyzing various correlation functions.
We study kinetic magnetism for the Fermi-Hubbard models in triangular type lattices, including a zigzag ladder, four- and six-legged triangular cylinders and a full two-dimensional triangular lattice. We focus on the regime of strong interactions, U≫tU\gg tU≫t and filling factors around one electron per site. For temperatures well above the hopping strength, the Curie-Weiss form of the magnetic susceptibility suggests effective antiferromagnetic correlations for systems that are hole doped with respect to ν=1ν=1ν=1, and ferromagnetic correlations for systems with electron dopings. We show that these correlations arise from magnetic polaron dressing of charge carrier propagating in a spin incoherent Mott insulator. Effective interactions corresponding to these correlations can strongly exceed the magnetic super-exchange energy. In the case of hole doping, antiferromagnetic polarons originate from kinetic frustration of individual holes in a triangular lattice. In the case of electron doping, Nagaoka type ferromagnetic correlations are induced by propagating doublons. These results provide a theoretical explanation of recent experimental results in moire TMDC materials. To understand many-body states arising from antiferromagentic polarons at low temperatures, we study hole doped systems in finite magnetic fields. At low dopings and intermediate magnetic fields we find a magnetic polaron phase, separated from the fully polarized state by a metamagnetic transition. With decreasing magnetic field the system shows a tendency to phase separate, with hole rich regions forming antiferromagnetic spinbags. We demonstrate that direct observations of magnetic polarons in triangular lattices can be achieved in experiments with ultracold atoms, which allow measurements of three point hole-spin-spin correlations.
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.