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arxiv: 2605.31240 · v1 · pith:YSE5ALZKnew · submitted 2026-05-29 · ❄️ cond-mat.str-el · cond-mat.mtrl-sci· cond-mat.quant-gas· quant-ph

Emergence of spin entanglement with the pseudogap onset in the Fermi-Hubbard model

Frederic Bippus , Thomas Chalopin , Gabriele Bellomia , Gerg\H{o} Ro\'osz , Titus Franz , Antoine Georges , Anna Kauch , Immanuel Bloch
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Karsten Held
This is my paper

Pith reviewed 2026-06-28 21:00 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mtrl-scicond-mat.quant-gasquant-ph
keywords Fermi-Hubbard modelpseudogapspin entanglementultracold atomsdynamical vertex approximationnearest-neighbor correlationsquantum simulator
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The pith

Spin-singlet entanglement between nearest-neighbor sites appears exactly when the pseudogap opens in the two-dimensional Fermi-Hubbard model.

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

The paper shows that in the Fermi-Hubbard model, spin-singlet entanglement between electrons turns on only at the temperature where the pseudogap regime begins. Classical spin correlations exist at higher temperatures, but the quantum entanglement stays strictly local to nearest neighbors once the pseudogap forms. This link is established by combining ultracold-atom experiments that directly measure entanglement with dynamical vertex approximation calculations on the lattice model. If correct, the result rules out descriptions of the pseudogap that rely solely on classical fluctuations and requires any microscopic theory to produce nearest-neighbor singlets at that scale.

Core claim

Using both an ultracold-atom quantum simulator and dynamical vertex approximation simulations, the authors find that spin-singlet entanglement emerges only as the pseudogap sets in and, unlike classical correlations, remains confined to nearest-neighbour sites in this regime. This observation disfavours purely classical-fluctuation theories of the pseudogap and constrains microscopic models to those that develop nearest-neighbour spin-singlet entanglement at the pseudogap onset.

What carries the argument

Direct measurement of spin-singlet entanglement via ultracold-atom protocols combined with dynamical vertex approximation calculations, which together track the temperature at which entanglement appears relative to the pseudogap crossover.

If this is right

  • The pseudogap cannot be explained by classical spin fluctuations alone.
  • Microscopic theories must generate nearest-neighbor spin singlets at the pseudogap temperature.
  • Entanglement remains short-ranged even while longer-range classical correlations may exist.
  • Quantum simulators can now probe entanglement as a diagnostic for the pseudogap regime.

Where Pith is reading between the lines

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

  • If the pseudogap is tied to local singlets, doping studies might show how entanglement evolves into d-wave pairing.
  • The same protocol could be applied to other models suspected of having pseudogap physics to test universality.
  • Numerical methods beyond dynamical vertex approximation could be benchmarked by whether they reproduce the entanglement onset.

Load-bearing premise

Both the dynamical vertex approximation and the ultracold-atom entanglement measurement faithfully reflect the true spin entanglement without large biases from the method or from finite-size or detection limitations.

What would settle it

An experiment or calculation that measures nearest-neighbor spin entanglement at temperatures well above the pseudogap onset temperature would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.31240 by Anna Kauch, Antoine Georges, Frederic Bippus, Gabriele Bellomia, Gerg\H{o} Ro\'osz, Immanuel Bloch, Karsten Held, Thomas Chalopin, Titus Franz.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p020_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p021_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p021_3.png] view at source ↗
read the original abstract

Despite decades of intense theoretical and experimental investigation, the two-dimensional Fermi-Hubbard model still resists a complete microscopic understanding. Conventional approaches typically probe global observables and locally resolved correlation functions. Here, we develop a complementary perspective based on the measurement of entanglement. Using both an ultracold-atom quantum simulator and numerical simulations based on the dynamical vertex approximation, we find that entanglement is closely tied to the onset of the enigmatic pseudogap regime: spin-singlet entanglement emerges only as the pseudogap sets in and, in contrast to classical correlations, remains confined to nearest-neighbour sites in this regime. Our results, therefore, disfavour purely classical-fluctuation theories of the pseudogap and constrain microscopic models to those that develop nearest-neighbour spin-singlet entanglement at the pseudogap onset.

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

2 major / 2 minor

Summary. The manuscript claims that in the 2D Fermi-Hubbard model, spin-singlet entanglement (witnessed by nearest-neighbor spin correlations <Si·Sj> < −1/4) emerges precisely at the onset of the pseudogap regime. This is shown via agreement between ultracold-atom quantum simulation and dynamical vertex approximation (DVA) calculations; unlike classical correlations, the entanglement remains confined to nearest-neighbor sites, disfavoring purely classical-fluctuation theories of the pseudogap.

Significance. If the central claim holds, the work supplies a new diagnostic linking the pseudogap directly to quantum entanglement rather than classical fluctuations, thereby constraining microscopic models of the Hubbard Hamiltonian. The deployment of two independent methods (experiment and DVA) is a clear strength that enhances credibility when quantitative agreement is demonstrated.

major comments (2)
  1. [DVA methods and results sections] The central claim that spin-singlet entanglement emerges exactly at pseudogap onset and remains NN-confined rests on DVA producing accurate local spin correlations below the pseudogap temperature. DVA approximates the two-particle vertex while treating the self-energy self-consistently; once the vertex becomes strongly momentum-dependent in the pseudogap regime, short-range antiferromagnetic fluctuations can be under- or overestimated. Because the entanglement witness is a sharp threshold on the same correlator (<Si·Sj> near −0.25), even modest systematic error can shift the apparent onset temperature or permit spurious longer-range entanglement. The manuscript should supply benchmarks of DVA spin correlators against exact methods or larger-cluster references in the relevant temperature window.
  2. [Abstract and main results] The abstract states that two independent methods agree on the entanglement-pseudogap link, yet provides no quantitative details on how the entanglement witness is extracted from either the ultracold-atom data or the DVA output, including error bars, finite-size scaling, or the precise temperature window used to identify the pseudogap onset. Without these, the reported coincidence of onsets cannot be assessed for robustness.
minor comments (2)
  1. [Introduction or methods] Notation for the spin correlator <Si·Sj> should be defined explicitly at first use, including the normalization convention (e.g., whether S are spin-1/2 operators).
  2. [Figure captions] Figure captions should state the lattice size, filling, and interaction strength U/t used for each data set to allow direct comparison between experiment and DVA.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the referee's thoughtful review and valuable suggestions. We have carefully considered the comments and provide point-by-point responses below. We will make revisions to enhance the clarity and robustness of our presentation.

read point-by-point responses

  1. Referee: [DVA methods and results sections] The central claim that spin-singlet entanglement emerges exactly at pseudogap onset and remains NN-confined rests on DVA producing accurate local spin correlations below the pseudogap temperature. DVA approximates the two-particle vertex while treating the self-energy self-consistently; once the vertex becomes strongly momentum-dependent in the pseudogap regime, short-range antiferromagnetic fluctuations can be under- or overestimated. Because the entanglement witness is a sharp threshold on the same correlator (<Si·Sj> near −0.25), even modest systematic error can shift the apparent onset temperature or permit spurious longer-range entanglement. The manuscript should supply benchmarks of DVA spin correlators against exact methods or larger-cluster references in the relevant temperature window.

    Authors: We appreciate the referee pointing out the potential limitations of DVA when the vertex develops strong momentum dependence. The manuscript relies on quantitative agreement between DVA and the ultracold-atom experiment for the local spin correlations as the primary validation. To strengthen the presentation, we will revise the methods section to include references to existing DVA benchmarks against exact diagonalization and cluster methods in the relevant temperature and doping range for the Hubbard model, and we will add a short discussion of why local correlators remain reliable even when longer-range fluctuations are approximated. This addresses the concern about possible shifts in the apparent onset without requiring new large-scale computations. revision: yes

  2. Referee: [Abstract and main results] The abstract states that two independent methods agree on the entanglement-pseudogap link, yet provides no quantitative details on how the entanglement witness is extracted from either the ultracold-atom data or the DVA output, including error bars, finite-size scaling, or the precise temperature window used to identify the pseudogap onset. Without these, the reported coincidence of onsets cannot be assessed for robustness.

    Authors: We agree that the abstract is too concise on these points and that explicit quantification improves assessability. The main text already describes the witness as nearest-neighbor <Si·Sj> < −1/4 and identifies the pseudogap onset via the temperature where the antinodal spectral function develops a gap, but we will revise both the abstract and the results section to state the error bars on the correlations, note the system sizes used for finite-size checks, and specify the temperature window (e.g., the range over which the pseudogap temperature is determined from the DVA self-energy and from the experimental compressibility or spectroscopy). These additions will make the coincidence of onsets more transparent without altering the central claim. revision: yes

Circularity Check

0 steps flagged

No circularity; results from independent experiment and DVA simulation

full rationale

The paper derives its claim that spin-singlet entanglement (witnessed by nearest-neighbor spin correlations below -1/4) emerges precisely at pseudogap onset from direct outputs of ultracold-atom measurements and dynamical vertex approximation calculations. These produce the underlying correlators without any fitted parameter that is then relabeled as a prediction, without self-definitional loops, and without load-bearing self-citations that would make the central result tautological. The distinction from classical correlations is likewise obtained from the same independent data streams rather than imposed by construction. This is the normal case of a self-contained numerical/experimental study.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the dynamical vertex approximation for capturing entanglement and on the fidelity of the quantum-simulator measurement of spin correlations.

axioms (1)
  • domain assumption Dynamical vertex approximation is sufficiently accurate for the Fermi-Hubbard model in the pseudogap regime
    Invoked for the numerical part of the study

pith-pipeline@v0.9.1-grok · 5708 in / 1170 out tokens · 26828 ms · 2026-06-28T21:00:41.091527+00:00 · methodology

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