arXiv:2512.01264 · Physical review. B./Physical review. B

Generalized Nagaoka ferromagnetism accompanied by flavor-selective Mott states in an SU ( N ) Fermi-Hubbard model

Juntaro Fujii, Kazuki Yamamoto, Akihisa Koga

Published Feb 24, 2026• 0 citations

Abstract

We study the ferromagnetic instability in an SU($N$) Fermi-Hubbard model on the hypercubic lattice. Combining dynamical mean-field theory with continuous-time quantum Monte Carlo simulations, we find that, in the strong-coupling regime at low temperatures, ferromagnetically ordered (FM) states develop away from the commensurate fillings. In the particle-doped SU($3$) system near one-third filling, the FM state is accompanied by a spontaneous flavor-selective Mott state, where two of the three flavors are Mott insulating while the remaining flavor is metallic. Since particles in the metallic flavor can almost freely move on the lattice without correlation effects, the ordered state is stabilized by the kinetic-energy gain of the doped particles. This is similar to the generalized Nagaoka ferromagnetism discussed in the one-hole-doped system at one-third filling. In the SU($4$) case, we find that six distinct types of FM states appear as the particle density varies. The results uncover the nature of the FM state in the SU($N$) Fermi-Hubbard systems and highlight the rich magnetic behavior enabled by enlarged internal symmetries.

DOI: 10.1103/kx3p-phyq

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arXiv:2512.01264 · Physical review. B./Physical review. B

Generalized Nagaoka ferromagnetism accompanied by flavor-selective Mott states in an SU ( N ) Fermi-Hubbard model

Juntaro Fujii, Kazuki Yamamoto, Akihisa Koga

Published Feb 24, 2026• 0 citations

arXiv HTML PDF

Abstract

We study the ferromagnetic instability in an SU(

N

) Fermi-Hubbard model on the hypercubic lattice. Combining dynamical mean-field theory with continuous-time quantum Monte Carlo simulations, we find that, in the strong-coupling regime at low temperatures, ferromagnetically ordered (FM) states develop away from the commensurate fillings. In the particle-doped SU(

3

) system near one-third filling, the FM state is accompanied by a spontaneous flavor-selective Mott state, where two of the three flavors are Mott insulating while the remaining flavor is metallic. Since particles in the metallic flavor can almost freely move on the lattice without correlation effects, the ordered state is stabilized by the kinetic-energy gain of the doped particles. This is similar to the generalized Nagaoka ferromagnetism discussed in the one-hole-doped system at one-third filling. In the SU(

4

) case, we find that six distinct types of FM states appear as the particle density varies. The results uncover the nature of the FM state in the SU(

N

) Fermi-Hubbard systems and highlight the rich magnetic behavior enabled by enlarged internal symmetries.

DOI: 10.1103/kx3p-phyq

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Sub-dimensional magnetic polarons in the one-hole doped SU(3) $t$ - $J$ modelSub-dimensional magnetic polarons in the one-hole doped SU(3) $t$-$J$ model

Henning Schlömer, Fabian Grusdt, Ulrich Schollwöck +2 more

The physics of doped Mott insulators is at the heart of strongly correlated materials and is believed to constitute an essential ingredient for high-temperature superconductivity. In systems with higher SU(N) spin symmetries, even richer magnetic ground states appear at a filling of one particle per site compared to the case of SU(2) spins, but their fate upon doping remains largely unexplored. Here we address this question by studying a single hole in the SU(3) $t$ - $J$ model, whose undoped ground state features long-range, diagonal spin stripes. By analyzing both ground state and dynamical properties utilizing the density matrix renormalization group, we establish the appearence of magnetic polarons consisting of chargons and flavor defects, whose dynamics is constrained to a single effective dimension along the ordered diagonal. We semi-analytically describe the system using geometric string theory, where paths of hole motion are the fundamental degrees of freedom. With recent advances in the realization and control of SU(N) Fermi-Hubbard models with ultracold atoms in optical lattices, our results can directly be observed in quantum gas microscopes with single-site resolution. Our work suggests the appearance of intricate ground states at finite doping constituted by emergent, coupled Luttinger liquids along diagonals, and is a first step towards exploring a wealth of physics in doped SU(N) Fermi-Hubbard models on various geometries.The physics of doped Mott insulators is at the heart of strongly correlated materials and is believed to constitute an essential ingredient for high-temperature superconductivity. In systems with higher SU(N) spin symmetries, even richer magnetic ground states appear at a filling of one particle per site compared to the case of SU(2) spins, but their fate upon doping remains largely unexplored. Here we address this question by studying a single hole in the SU(3) $t$-$J$ model, whose undoped ground state features long-range, diagonal spin stripes. By analyzing both ground state and dynamical properties utilizing the density matrix renormalization group, we establish the appearence of magnetic polarons consisting of chargons and flavor defects, whose dynamics is constrained to a single effective dimension along the ordered diagonal. We semi-analytically describe the system using geometric string theory, where paths of hole motion are the fundamental degrees of freedom. With recent advances in the realization and control of SU(N) Fermi-Hubbard models with ultracold atoms in optical lattices, our results can directly be observed in quantum gas microscopes with single-site resolution. Our work suggests the appearance of intricate ground states at finite doping constituted by emergent, coupled Luttinger liquids along diagonals, and is a first step towards exploring a wealth of physics in doped SU(N) Fermi-Hubbard models on various geometries.

arXiv:2312.14137Dec 21, 20231 citation

We study the ferromagnetic instability in an SU(

N

3

4

) case, we find that six distinct types of FM states appear as the particle density varies. The results uncover the nature of the FM state in the SU(

N

) Fermi-Hubbard systems and highlight the rich magnetic behavior enabled by enlarged internal symmetries.

\frac{1}{3}

filling, modeling fermions with three possible spin flavors moving on a square lattice with an average of one particle per site. We provide clear evidence of a quantum critical point separating a nonmagnetic uniform metallic phase from a regime where long-range ``spin'' order is present. This discovery of multiple successive transitions to magnetic states with regular, long-range alternation of the different flavors, whose symmetry changes as the interaction strength increases, significantly extends previous work in the Heisenberg limit to itinerant fermions. In addition to the rich quantum magnetism, this important physical system allows one to study integer filling and the associated Mott transition disentangled from nesting, in contrast to the usual SU(2) model, while preserving the square-lattice geometry. Our results also provide a significant step towards the interpretation of present and future experiments on fermionic alkaline-earth atoms, and other realizations of

\mathrm{SU}(N)

physics.

We provide numerical evidence of the Nagaoka's theorem in the

\mathrm{SU}(N)

Fermi-Hubbard model on various cluster geometries, such as the square, the honeycomb, and the triangular lattices. In particular, by diagonalizing several finite-size clusters, we show that for one hole away from filling

1/N

, the itinerant ferromagnetism arises for

U

(the positive on-site interaction) larger than

{U}_{c}

(the value at the transition), which depends strongly on the coordination number

z

and on

N

, the number of degenerate orbitals, that we vary from

N=2

to 6 in our simulations. We prove that

{U}_{c}

is a nondecreasing function of

N

. In addition, we find that the lattice dependency is rooted in the kinetic energy of the hole. We find that large coordination numbers

z

lower the value of

{U}_{c}

. Complementary, we explore the effect of long-range hopping on the appearance of itinerant ferromagnetism, and we demonstrate that it acts as an increased coordination number, protecting the ferromagnetic phase at small

U

. Finally, the effects of both the presence of some additional holes and the finite size of the clusters are briefly discussed.

Sub-dimensional magnetic polarons in the one-hole doped SU(3)

t

J

model

t

J

model, whose undoped ground state features long-range, diagonal spin stripes. By analyzing both ground state and dynamical properties utilizing the density matrix renormalization group, we establish the appearence of magnetic polarons consisting of chargons and flavor defects, whose dynamics is constrained to a single effective dimension along the ordered diagonal. We semi-analytically describe the system using geometric string theory, where paths of hole motion are the fundamental degrees of freedom. With recent advances in the realization and control of SU(N) Fermi-Hubbard models with ultracold atoms in optical lattices, our results can directly be observed in quantum gas microscopes with single-site resolution. Our work suggests the appearance of intricate ground states at finite doping constituted by emergent, coupled Luttinger liquids along diagonals, and is a first step towards exploring a wealth of physics in doped SU(N) Fermi-Hubbard models on various geometries.