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arxiv: 2510.01909 · v3 · submitted 2025-10-02 · ❄️ cond-mat.str-el

Bad metal behavior and Lifshitz transition of a Nagaoka ferromagnet

Jonas Arnold , Peter Kopietz , Andreas R\"uckriegel This is my paper

Pith reviewed 2026-05-18 10:43 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords Hubbard modelNagaoka ferromagnetfunctional renormalization groupLifshitz transitionbad metalinfinite repulsionsquare latticespectral function
0
0 comments X

The pith

The infinite-U Hubbard model on the square lattice hosts an extended Nagaoka ferromagnet with bad-metal behavior separated by a Lifshitz transition.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper extends the fermionic functional renormalization group to handle projected Hilbert spaces arising from strong correlations. It applies the method to the Hubbard model with infinite on-site repulsion on a square lattice with nearest-neighbor hopping. The ground state evolves from a paramagnetic Fermi liquid at low densities through antiferromagnetic stripe order at intermediate densities to a Nagaoka ferromagnet at high densities. The spectral function in the ferromagnetic phase is flat and broad, indicating incoherent non-Fermi-liquid behavior. Two ferromagnetic regimes are separated by a Lifshitz transition that changes the Fermi-surface character.

Core claim

For a square lattice with nearest-neighbor hopping 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. Two distinct ferromagnetic regimes are separated by a Lifshitz transition.

What carries the argument

Extended fermionic functional renormalization group flow in the projected Hilbert space, which determines the density-dependent phase diagram and single-particle spectral functions.

If this is right

  • The high-density Nagaoka ferromagnet displays bad-metal behavior via its flat, broad single-particle band.
  • A Lifshitz transition splits the ferromagnetic phase into two regimes with different Fermi-surface topologies.
  • Antiferromagnetic stripe order appears as a stable intermediate phase before ferromagnetism dominates.
  • The paramagnetic Fermi liquid remains stable only at low electron densities.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar Lifshitz transitions and spectral features may appear in other lattices or with next-nearest-neighbor hopping.
  • The broad incoherent spectrum could be probed by ARPES in materials approximating the infinite-U limit.
  • Finite-temperature extensions might reveal how thermal fluctuations destroy these ordered phases.
  • The overall density-driven sequence could inform models of doped Mott insulators near superconductivity.

Load-bearing premise

The truncation and regulator choices in the renormalization-group flow remain accurate enough across the full density range to yield reliable phase boundaries and spectral functions.

What would settle it

Comparison of the predicted density window for the Nagaoka ferromagnet and the location of the Lifshitz transition against exact diagonalization or large-scale DMRG calculations on the same model.

Figures

Figures reproduced from arXiv: 2510.01909 by Andreas R\"uckriegel, Jonas Arnold, Peter Kopietz.

Figure 1
Figure 1. Figure 1: FIG. 1. Ground state phase diagriam of the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Graphical representation of the flow equations for (a) [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Brillouin zone plots of the static part of the magnetic [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Electronic spectral properties for (a) [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript extends the fermionic functional renormalization group to projected Hilbert spaces and applies it to the infinite-U Hubbard model on the square lattice. It reports a density-driven evolution of the ground state from a paramagnetic Fermi liquid at low filling, through an antiferromagnetic stripe phase at intermediate densities, to an extended Nagaoka ferromagnet at high densities. The single-particle spectral function of the Nagaoka phase is found to contain a flat but broad band indicative of incoherent non-Fermi-liquid behavior, and two distinct ferromagnetic regimes are separated by a Lifshitz transition.

Significance. If the fRG results prove robust, the work would supply concrete numerical evidence for the structure of the Nagaoka ferromagnet and for the emergence of bad-metal spectral features in a controlled microscopic setting. The methodological extension itself is a useful technical step for treating projected spaces within fRG. The reported Lifshitz transition and the quantitative location of phase boundaries constitute falsifiable predictions that could be compared with other numerical or experimental probes.

major comments (1)
  1. [Method section describing the fRG extension] The truncation scheme, frequency dependence, and regulator implementation for the extended fRG flow in the projected Hilbert space are only sketched. Because the reported phase boundaries, the location of the Lifshitz transition, and the width of the flat band are extracted directly from these flows, a quantitative assessment of truncation error (e.g., comparison with exact diagonalization or DMFT in limiting regimes, or explicit checks of regulator independence) is required to establish that the central claims are not artifacts of the approximation.
minor comments (1)
  1. [Title and abstract] The title refers to 'bad metal behavior' while the abstract and results emphasize an 'incoherent non-Fermi liquid'; a brief clarification of the relation between these characterizations would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive evaluation of the significance of our results and for the detailed comment on the methodological presentation. We address the concern point by point below and will revise the manuscript to strengthen the technical description and supporting checks.

read point-by-point responses

  1. Referee: [Method section describing the fRG extension] The truncation scheme, frequency dependence, and regulator implementation for the extended fRG flow in the projected Hilbert space are only sketched. Because the reported phase boundaries, the location of the Lifshitz transition, and the width of the flat band are extracted directly from these flows, a quantitative assessment of truncation error (e.g., comparison with exact diagonalization or DMFT in limiting regimes, or explicit checks of regulator independence) is required to establish that the central claims are not artifacts of the approximation.

    Authors: We agree that the method section in the submitted manuscript provides a concise rather than exhaustive account of the truncation, frequency treatment, and regulator. In the revised version we will expand this section with an explicit statement of the vertex truncation (including the frequency grid and the neglect of higher-order frequency structures), the precise form of the regulator adapted to the projected space, and the flow equations used. We will also add a dedicated subsection presenting regulator-independence tests: results for the phase boundaries and the flat-band width will be shown for two qualitatively different cutoff functions (sharp and smooth) at representative densities. For truncation-error assessment we will include a direct comparison with DMFT in the low-density paramagnetic regime, where the infinite-U constraint is less severe and DMFT data are readily available; this benchmark confirms that the paramagnetic Fermi-liquid regime and its spectral features are reproduced. Direct ED comparisons remain limited by system size, but the added regulator and DMFT checks provide quantitative support that the reported Lifshitz transition and incoherent flat band are not artifacts of the specific truncation chosen. revision: yes

Circularity Check

0 steps flagged

No circularity: numerical fRG flow yields independent results

full rationale

The paper computes the phase diagram and spectral function via direct numerical integration of extended fermionic fRG flow equations in the projected infinite-U Hilbert space. No step reduces by construction to a fitted parameter, self-defined quantity, or load-bearing self-citation chain; the Lifshitz transition and broad incoherent band emerge from the density-dependent flow across the full range rather than being imposed by internal definitions or prior author results treated as axioms. The method extension is presented as a technical development whose accuracy is an assumption open to external benchmarks, not a tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper rests on the standard infinite-U Hubbard Hamiltonian on the square lattice and on the validity of the extended fRG truncation for projected spaces; no additional free parameters or invented entities are stated in the abstract.

axioms (2)
  • domain assumption The infinite on-site repulsion projects the Hilbert space by forbidding double occupancy.
    Stated in the abstract as the model under study.
  • ad hoc to paper The extended fermionic fRG flow equations remain quantitatively reliable for the projected space across the density range examined.
    This is the central methodological assumption required for the reported phase diagram and spectral functions.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Functional renormalization group for extremely correlated electrons

    cond-mat.str-el 2025-12 unverdicted novelty 6.0

    Strong-coupling FRG for the U=∞ Hubbard model shows bandwidth and quasiparticle residue decreasing with density, polaronic continua, bad-metal behavior with magnetic correlations, and Luttinger theorem violation above...

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