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arXiv:2510.01909 · Physical Review Letters

Bad Metal Behavior and Lifshitz Transition of a Nagaoka Ferromagnet

Anonymous, Peter Kopietz, Andreas Rückriegel

Published Aug 5, 2026• 1 citation
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Abstract

Using an extension of the fermionic functional renormalization group for systems where strong correlations give rise to projected Hilbert spaces, we calculate the phase diagram and the electronic spectral function of the Hubbard model at infinite on-site repulsion. For a square lattice with nearest-neighbor hopping we find that the ground state evolves from a paramagnetic Fermi liquid at low densities via a state with antiferromagnetic stripe order at intermediate densities to an extended Nagaoka ferromagnet at high densities. The single-particle spectral function of the Nagaoka ferromagnet exhibits a flat but rather broad band characteristic for an incoherent non-Fermi liquid. We identify two distinct ferromagnetic regimes separated by a Lifshitz transition.

DOI
10.1103/py7g-jz2x

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Using an extension of the fermionic functional renormalization group for systems where strong correlations give rise to projected Hilbert spaces, we calculate the phase diagram and the electronic spectral function of the Hubbard model at infinite on-site repulsion. For a square lattice with nearest-neighbor hopping we find that the ground state evolves from a paramagnetic Fermi liquid at low densities via a state with antiferromagnetic stripe order at intermediate densities to an extended Nagaoka ferromagnet at high densities. The single-particle spectral function of the Nagaoka ferromagnet exhibits a flat but rather broad band characteristic for an incoherent non-Fermi liquid. We identify two distinct ferromagnetic regimes separated by a Lifshitz transition.
At strong on-site repulsion $ U $, the fermionic Hubbard model realizes an extremely correlated electron system. In this regime, it is natural to derive the low-energy physics with the help of non-canonical operators acting on a projected Hilbert space without double occupancies. Using a strong-coupling functional renormalization group technique, we study the physics of such extreme correlations in the strict $ U = \infty $ limit, where only kinematic interactions due to the Hilbert space projection remain. For nearest-neighbor hopping on a square lattice, we find that the electronic spectrum is significantly renormalized, with bandwidth and quasi-particle residue strongly decreasing with increasing electron density. On the other hand, damping and particle-hole asymmetry increase, while a polaronic continuum forms in the hole sector, below the single-particle band. Fermi liquid phenomenology applies only at low densities, where the system remains paramagnetic. At higher densities, we find a bad metal with strong magnetic correlations, indicating that the ground state is the Nagaoka ferromagnet at high densities and a stripe antiferromagnet at intermediate densities. Both in the paramagnetic and the ferromagnetic regimes, we observe a violation of Luttinger's theorem.
We study the phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping using exact diagonalization, the density-matrix renormalization group, the Edwards variational ansatz, and an adaptation of weak-coupling calculations on the two-chain Hubbard model. We find that a substantial region of the strong-coupling phase diagram is ferromagnetic, and that three physically different limiting cases are connected in one ferromagnetic phase. At a point in the phase diagram at which there are two Fermi points at weak coupling, we study carefully the phase transition from the paramagnetic state to the fully polarized one as a function of the on-site Coulomb repulsion. We present evidence that the transition is second order and determine the critical exponents numerically. In this parameter regime, the system can be described as a Luttinger liquid at weak coupling. We extract the Luttinger-liquid parameters and show how their behavior differs from that of the nearest-neighbor Hubbard model. The general weak-coupling phase diagram can be mapped onto that of the two-chain Hubbard model. We exhibit explicitly the adapted phase diagram and determine its validity by numerically calculating spin and charge gaps using the density-matrix renormalization group.
A wide variety of experimental platforms, ranging from semiconductor quantum-dot arrays to moiré materials, have recently emerged as powerful quantum simulators for studying the Hubbard model and its variants. Motivated by these developments, here, we investigate a generalization of the Hubbard model which includes the effects of long-range Coulomb interactions. Working on finite-sized two-dimensional square and triangular lattices, we use exact diagonalization and density-matrix renormalization group calculations to probe the magnetic structure of the ground state in the strong-coupling regime, where UUU (the onsite repulsion) ≫\gg≫ ttt (the nearest-neighbor hopping). For small electron dopings above the half-filled antiferromagnet, we numerically uncover a rich variety of magnetically ordered states, and in conjunction with theoretical arguments, infer the phase diagram of the system as a function of doping and interaction strengths. In particular, we find that the inclusion of long-range Coulomb interactions induces an instability of high-spin states$\unicode{x2014}$such as the saturated Nagaoka ferromagnet$\unicode{x2014}$towards phase separation and stripe ordering. We also present proposals for the observation of some of our key findings in experiments that would shed further light on this paradigmatic strongly correlated system.
We study the magnetic properties of the two-dimensional Hubbard model with nearest-neighbor (t) and next-nearest-neighbor (t2{t}_{2}t2​) hopping and on-site repulsion U. We first calculate the mean-field phase diagram as a function of band filling and U. Because of the Van Hove singularity in the density of states, we find a ferromagnetic phase extending to zero U for certain band filling. For the half-filled band case, antiferromagnetism sets in at a finite value of U if t2{t}_{2}t2​\ensuremath{\ne}0. We study the behavior of spin-spin correlation functions for small lattices of up to N=64 atoms using Monte Carlo simulations, as well as exact diagonalization for N=4. Our results show enhanced ferromagnetic correlations in some regions, but apparently no ferromagnetic long-range order. In the half-filled case, our numerical results are consistent with a nonzero critical U. For a non-half-filled band our results suggest that there is no long-range order.
We study the one-dimensional Hubbard model with nearest-neighbor and next-nearest-neighbor hopping integrals by using the density-matrix renormalization group method and Hartree-Fock approximation. Based on the calculated results for the spin gap, total-spin quantum number, and Tomonaga-Luttinger-liquid parameter, we determine the ground-state phase diagram of the model in the entire filling and wide parameter region. We show that, in contrast to the weak-coupling regime where a spin-gapped liquid phase is predicted in the region with four Fermi points, the spin gap vanishes in a substantial region in the strong-coupling regime. It is remarkable that a large variety of phases, such as the paramagnetic metallic phase, spin-gapped liquid phase, singlet and triplet superconducting phases, and fully polarized ferromagnetic phase, appear in such a simple model in the strong-coupling regime.
Using a cluster extension of the dynamical mean-field theory (CDMFT) we map out the magnetic phase diagram of the anisotropic square lattice Hubbard model with nearest-neighbor intrachain ttt and interchain ${t}_{\ensuremath{\perp}}$ hopping amplitudes at half filling. A fixed value of the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}=\ensuremath{-}{t}_{\ensuremath{\perp}}/2$ removes the nesting property of the Fermi surface and stabilizes a paramagnetic metal phase in the weak-coupling regime. In the isotropic and moderately anisotropic regions, a growing spin entropy in the metal phase is quenched out at a critical interaction strength by the onset of long-range antiferromagnetic (AF) order of preformed local moments. It gives rise to a first-order metal-insulator transition consistent with the Mott-Heisenberg picture. In contrast, a strongly anisotropic regime ${t}_{\ensuremath{\perp}}/t\ensuremath{\lesssim}0.3$ displays a quantum critical behavior related to the continuous transition between an AF metal phase and the AF insulator. Hence, within the present framework of CDMFT, the opening of the charge gap is magnetically driven as advocated in the Slater picture. We also discuss how the lattice-anisotropy-induced evolution of the electronic structure on a metallic side of the phase diagram is tied to the emergence of quantum criticality.