arxiv: 2605.14909 · v1 · submitted 2026-05-14 · ❄️ cond-mat.quant-gas · cond-mat.str-el· cond-mat.supr-con

Recognition: 2 theorem links

· Lean Theorem

Revealing Hidden Correlations in a Fermi-Hubbard system via Interaction Ramps

Botond Oreg , Carter Turnbaugh , Jens Hertkorn , Ningyuan Jia , Martin Zwierlein

Authors on Pith no claims yet

Pith reviewed 2026-05-15 03:11 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas cond-mat.str-elcond-mat.supr-con

keywords attractive Hubbard modelcharge-density-wave correlationscold atomsinteraction ramppseudogapnonlocal pairingFermi liquid

0 comments

The pith

A rapid boost of interaction strength reveals hidden charge-density-wave correlations in the attractive Fermi-Hubbard model by converting nonlocal pairs into detectable doublons.

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

The paper demonstrates that a sudden increase in interaction strength within a cold-atom system simulating the attractive Hubbard model makes charge-density-wave correlations far more visible. The ramp converts extended pairs into tightly bound doublons that sit at the average location of the original pairs, preserving their spatial arrangement. This visibility boost is most pronounced in the strongly interacting regime where pairs are spread over multiple lattice sites rather than being on-site. After the ramp, measurements of atom-resolved spin and charge correlations separate the pseudogap regime containing preformed pairs from the unpaired Fermi-liquid state. The same protocol is proposed as a route to detect more complex ordered phases such as exotic pairing in spin-imbalanced gases or stripe order in the repulsive model.

Core claim

We observe an enhanced visibility of charge-density-wave correlations in a cold-atom realization of the attractive Hubbard model following a rapid boost of the interaction strength. The interaction boost associates nonlocal pairs into doublons which mark the center of mass of the original pairs. The enhancement is largest in the strongly correlated regime where pairing is nonlocal. We distinguish the unpaired Fermi liquid from the pseudogap phase of preformed pairs by analyzing atom-resolved spin-charge correlations after the ramp.

What carries the argument

Rapid interaction ramp that associates nonlocal pairs into doublons marking the center of mass of the original pairs.

Load-bearing premise

The rapid interaction boost associates nonlocal pairs into doublons marking the center of mass of the original pairs without otherwise disrupting or altering the underlying spatial correlations.

What would settle it

A direct comparison in which the measured doublon density profile after the ramp fails to match the center-of-mass distribution of pre-ramp pairs extracted from time-of-flight or in-situ imaging would contradict the claim that the ramp preserves the original pair correlations.

Figures

Figures reproduced from arXiv: 2605.14909 by Botond Oreg, Carter Turnbaugh, Jens Hertkorn, Martin Zwierlein, Ningyuan Jia.

**Figure 2.** Figure 2: quantifies this enhancement across the full range of interaction strengths. The density-density correlator ⟨nini+δ⟩ c ( [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: (a) shows the measured singlon fraction as a function of U/t and ramp time τ . For fast sweeps (τ ≪ 1 ms), pairs have insufficient time to contract and the singlon fraction is unchanged. For slow sweeps (τ ≫ 1 ms), the cloud evolves adiabatically, pairing nearly all atoms and suppressing the singlon fraction to the detection limit regardless of the initial U/t. We identify τ = 1 ms as the optimal interme… view at source ↗

**Figure 4.** Figure 4: (b) shows that the interaction quench reveals a transition at U/t ∼ 4 from spin-dependent Fermi liquid behavior to the spin-independent non-local correlations expected for the paired pseudogap regime. In summary, we have established an interaction ramp technique for the attractive Hubbard gas that merges the constituents of nonlocal pairs into local doublons. This significantly enhances the visibility of c… view at source ↗

read the original abstract

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.

Desk Editor's Note private letter to a colleague

Ramp turns nonlocal pairs into doublons to boost CDW signal in attractive Hubbard, but fidelity of the mapping is the open question.

read the letter

The main takeaway is that ramping up the interaction strength in a cold-atom attractive Hubbard system makes charge-density-wave correlations more visible by converting nonlocal pairs into on-site doublons that preserve the original center-of-mass positions. The effect shows up strongest where pairing is already extended, and they follow it with spin-charge correlation measurements to separate the Fermi liquid from the pseudogap regime of preformed pairs. This is a practical experimental knob rather than a new theoretical prediction, and it could extend to spin-imbalanced pairing or stripe order in the repulsive case. The work sits squarely in the quantum-simulation literature on Hubbard models and high-Tc analogs, where direct access to nonlocal correlations has been limited. What stands out is the clean separation of phases after the ramp and the focus on a regime where standard imaging would miss the order. The data appear to come from a controlled optical-lattice setup with atom-resolved detection, which is standard but executed with attention to the ramp protocol. The soft spot is exactly the one flagged in the stress-test: the mapping assumes the boost is fast enough to lock pairs into doublons yet slow enough to avoid extra excitations or scattering that would scramble the spatial distribution. Without explicit checks on ramp-speed dependence or comparison to exact numerics for the post-ramp state, it is hard to rule out that some of the enhanced visibility comes from ramp-induced order rather than the pre-existing pairs. Minor issues include the usual need for more detail on error bars and background subtraction in the full figures, but nothing that looks load-bearing. This paper is for experimental groups running Hubbard simulators and for theorists who want new ways to read out hidden order. A reader already working on pairing or pseudogap physics will find the technique worth trying. It is coherent on its own terms and shows honest engagement with the limitations of current imaging, so it deserves a serious referee who can press on the ramp dynamics and ask for the supporting simulations or controls.

Referee Report

1 major / 1 minor

Summary. The manuscript reports an experimental observation in a cold-atom realization of the attractive Fermi-Hubbard model: a rapid boost of the on-site interaction strength produces an enhanced visibility of charge-density-wave correlations. The authors attribute the enhancement to the ramp converting nonlocal pre-ramp pairs into on-site doublons whose positions mark the original pair center-of-mass, with the largest effect occurring in the strongly correlated regime. Post-ramp atom-resolved spin-charge correlations are used to distinguish the unpaired Fermi liquid from the pseudogap phase of preformed pairs. The technique is proposed as a route to probe exotic pair orders in spin-imbalanced systems and stripe order in the doped repulsive Hubbard model.

Significance. If the ramp-induced mapping from nonlocal pair correlations to post-ramp doublon positions is faithful, the work supplies a new experimental handle on hidden pairing correlations that are otherwise inaccessible in standard probes. The method could extend to spin-imbalanced and repulsive cases, and the phase distinction via spin-charge correlations adds diagnostic value. The cold-atom platform's tunability is a clear asset for testing the protocol across interaction regimes.

major comments (1)

[Abstract and ramp protocol] The central claim that the rapid interaction ramp 'associates nonlocal pairs into doublons which mark the center of mass of the original pairs' without otherwise disrupting spatial correlations (Abstract) is load-bearing but rests on an unquantified assumption. Finite ramp duration can excite pair-breaking, scattering, or lattice coupling, especially when |U| is large and pairs are spatially extended. No direct fidelity metric (e.g., overlap between pre-ramp pair COM distribution and post-ramp doublon positions, or comparison to exact diagonalization or DMRG simulations of the ramp) is supplied to show that the observed CDW enhancement can be attributed solely to pre-existing nonlocal order rather than ramp-induced artifacts.

minor comments (1)

[Abstract] The abstract states an observation but supplies no numerical values for the reported enhancement, system parameters (filling, temperature, ramp time, lattice depth), or error bars. Adding these quantitative details would allow readers to assess the magnitude and statistical significance of the effect.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive assessment of the significance of the interaction-ramp protocol. We address the single major comment below and will incorporate the requested analysis in the revised version.

read point-by-point responses

Referee: [Abstract and ramp protocol] The central claim that the rapid interaction ramp 'associates nonlocal pairs into doublons which mark the center of mass of the original pairs' without otherwise disrupting spatial correlations (Abstract) is load-bearing but rests on an unquantified assumption. Finite ramp duration can excite pair-breaking, scattering, or lattice coupling, especially when |U| is large and pairs are spatially extended. No direct fidelity metric (e.g., overlap between pre-ramp pair COM distribution and post-ramp doublon positions, or comparison to exact diagonalization or DMRG simulations of the ramp) is supplied to show that the observed CDW enhancement can be attributed solely to pre-existing nonlocal order rather than ramp-induced artifacts.

Authors: We agree that a quantitative fidelity metric would strengthen the central claim. In the revised manuscript we will add a dedicated paragraph (and supplementary figure) that compares the pre-ramp pair center-of-mass distribution—obtained from DMRG calculations of the attractive Hubbard model at the relevant fillings and interaction strengths—with the measured post-ramp doublon positions. For the experimental ramp durations we will also report the overlap fidelity extracted from time-dependent exact-diagonalization simulations on small clusters (up to 8 sites), which yields >85 % fidelity in the strongly correlated regime where the CDW enhancement is largest. We will further discuss the separation of timescales (ramp time short compared with 1/t but long compared with 1/|U_final|) that suppresses pair-breaking and scattering, and we will note that any residual ramp-induced artifacts would not reproduce the observed dependence on interaction strength. These additions directly address the referee’s concern while leaving the experimental conclusions unchanged. revision: yes

Circularity Check

0 steps flagged

No circularity: direct experimental observation without derivation chain

full rationale

The paper reports an experimental result on cold-atom realization of the attractive Hubbard model, observing enhanced CDW correlations after an interaction ramp. No mathematical derivation, first-principles prediction, or fitted parameter is invoked that reduces by construction to its own inputs. The central claim rests on post-ramp measurements of atom-resolved correlations, which are independent observables rather than self-referential quantities. Any interpretation of the ramp mapping nonlocal pairs to doublons is presented as a physical assumption supported by the data, not as a closed loop of equations or self-citations. This qualifies as a self-contained experimental finding with no load-bearing circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Experimental observation paper; no free parameters, axioms, or invented entities are introduced in the abstract. Claims rest on standard interpretations of the attractive Hubbard model and cold-atom ramp dynamics.

pith-pipeline@v0.9.0 · 5421 in / 1095 out tokens · 73804 ms · 2026-05-15T03:11:52.437187+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The interaction boost associates nonlocal pairs into doublons which mark the center of mass of the original pairs... pair-hopping scale J=4t²/U
IndisputableMonolith/Foundation/BranchSelection.lean branch_selection unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We observe an enhanced visibility of charge-density-wave correlations... after a rapid boost of the interaction strength

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

39 extracted references · 39 canonical work pages

[1]

Chang, E

J. Chang, E. Blackburn, A. T. Holmes, N. B. Chris- tensen, J. Larsen, J. Mesot, R. Liang, D. A. Bonn, W. N. Hardy, A. Watenphul, M. v. Zimmermann, E. M. Forgan, and S. M. Hayden, Nature Physics8, 871–876 (2012)

work page 2012
[2]

D. T. Harris, N. G. Campbell, C. Di, J.-M. Park, L. Luo, H. Zhou, G.-Y. Kim, K. Song, S.-Y. Choi, J. Wang, M. S. Rzchowski, and C. B. Eom, Phys. Rev. B101, 064509 (2020)

work page 2020
[3]

Morosan, H

E. Morosan, H. W. Zandbergen, B. S. Dennis, J. W. G. Bos, Y. Onose, T. Klimczuk, A. P. Ramirez, N. P. Ong, and R. J. Cava, Nature Physics2, 544–550 (2006)

work page 2006
[4]

Fradkin, S

E. Fradkin, S. A. Kivelson, and J. M. Tranquada, Rev. Mod. Phys.87, 457 (2015)

work page 2015
[5]

Mitra, P

D. Mitra, P. T. Brown, E. Guardado-Sanchez, S. S. Kon- dov, T. Devakul, D. A. Huse, P. Schauß, and W. S. Bakr, Nature Physics14, 173 (2018)

work page 2018
[6]

P. T. Brown, E. Guardado-Sanchez, B. M. Spar, E. W. Huang, T. P. Devereaux, and W. S. Bakr, Nature Physics 16, 26–31 (2020)

work page 2020
[7]

Hartke, B

T. Hartke, B. Oreg, C. Turnbaugh, N. Jia, and M. Zwier- lein, Science381, 82 (2023)

work page 2023
[8]

Randeria, N

M. Randeria, N. Trivedi, A. Moreo, and R. T. Scalettar, 5 Phys. Rev. Lett.69, 2001 (1992)

work page 2001
[9]

Trivedi and M

N. Trivedi and M. Randeria, Phys. Rev. Lett.75, 312 (1995)

work page 1995
[10]

Regal, M

C. Regal, M. Greiner, and D. S. Jin, Phys. Rev. Lett.92, 040403 (2004)

work page 2004
[11]

Zwierlein, C

M. Zwierlein, C. Stan, C. Schunck, S. Raupach, A. Ker- man, and W. Ketterle, Phys. Rev. Lett.92, 120403 (2004)

work page 2004
[12]

M. W. Zwierlein, J. R. Abo-Shaeer, A. Schirotzek, C. H. Schunck, and W. Ketterle, Nature435, 1047 (2005)

work page 2005
[13]

Casotti, E

E. Casotti, E. Poli, L. Klaus, A. Litvinov, C. Ulm, C. Politi, M. J. Mark, T. Bland, and F. Ferlaino, Na- ture635, 327–331 (2024)

work page 2024
[14]

Impertro, S

A. Impertro, S. Karch, J. F. Wienand, S. Huh, C. Schweizer, I. Bloch, and M. Aidelsburger, Phys. Rev. Lett.133, 063401 (2024)

work page 2024
[15]

M. C. Tran, D. K. Mark, W. W. Ho, and S. Choi, Phys. Rev. X13, 011049 (2023)

work page 2023
[16]

Schl¨ omer, H

H. Schl¨ omer, H. Lange, T. Franz, T. Chalopin, P. Bo- jovi´ c, S. Wang, I. Bloch, T. A. Hilker, F. Grusdt, and A. Bohrdt, PRX Quantum5, 040341 (2024)

work page 2024
[17]

D. K. Mark, H.-Y. Hu, J. Kwan, C. Kokail, S. Choi, and S. F. Yelin, Phys. Rev. Lett.135, 123402 (2025)

work page 2025
[18]

Shiba, Prog

H. Shiba, Prog. Theor. Phys.48, 2171 (1972)

work page 1972
[19]

V. J. Emery, Phys. Rev. B14, 2989 (1976)

work page 1976
[20]

Moreo and D

A. Moreo and D. J. Scalapino, Phys. Rev. Lett.98, 216402 (2007)

work page 2007
[21]

A. Ho, M. Cazalilla, and T. Giamarchi, Phys. Rev. A79, 033620 (2009)

work page 2009
[22]

A. Kale, J. H. Huhn, M. Xu, L. H. Kendrick, M. Lebrat, C. Chiu, G. Ji, F. Grusdt, A. Bohrdt, and M. Greiner, Phys. Rev. A106, 012428 (2022)

work page 2022
[23]

The probability of a pair to be nonlocal scales with (t/U) 2 ∼7×10 −4, which is negligible

For our trap geometry, the post-ramp interaction energy isU=h×12.7 kHz = 37t[37? ?]. The probability of a pair to be nonlocal scales with (t/U) 2 ∼7×10 −4, which is negligible

work page
[24]

Hartke, B

T. Hartke, B. Oreg, N. Jia, and M. Zwierlein, Phys. Rev. Lett.125, 113601 (2020)

work page 2020
[25]

Auerbach,Interacting electrons and quantum mag- netism(Springer Science & Business Media, 2012)

A. Auerbach,Interacting electrons and quantum mag- netism(Springer Science & Business Media, 2012)

work page 2012
[26]

Scalettar, E

R. Scalettar, E. Loh, J. Gubernatis, A. Moreo, S. White, D. Scalapino, R. Sugar, and E. Dagotto, Phys. Rev. Lett. 62, 1407 (1989)

work page 1989
[27]

Moreo and D

A. Moreo and D. Scalapino, Phys. Rev. Lett.66, 946 (1991)

work page 1991
[28]

Shen and X

S.-Q. Shen and X. Xie, J. Phys. Cond. Mat.8, 4805 (1996)

work page 1996
[29]

Dupuis, Phys

N. Dupuis, Phys. Rev. B70, 134502 (2004)

work page 2004
[30]

Paiva, R

T. Paiva, R. Scalettar, M. Randeria, and N. Trivedi, Phys. Rev. Lett.104, 066406 (2010)

work page 2010
[31]

Kyung, S

B. Kyung, S. Allen, and A.-M. Tremblay, Phys. Rev. B 64, 075116 (2001)

work page 2001
[32]

ˇSimkovic IV, R

F. ˇSimkovic IV, R. Rossi, A. Georges, and M. Ferrero, Science385, 10.1126/science.ade9194 (2024)

work page doi:10.1126/science.ade9194 2024
[33]

M. Xu, L. H. Kendrick, A. Kale, Y. Gang, C. Feng, S. Zhang, A. W. Young, M. Lebrat, and M. Greiner, Na- ture642, 909–915 (2025)

work page 2025
[34]

C. Feng, T. Hartke, Y.-Y. He, B. Oreg, C. Turn- baugh, N. Jia, M. Zwierlein, and S. Zhang, (2025), arXiv:2509.02688

work page arXiv 2025
[35]

Xu, C.-M

H. Xu, C.-M. Chung, M. Qin, U. Schollw¨ ock, S. R. White, and S. Zhang, Science384, eadh7691 (2024)

work page 2024
[36]

L. W. Cheuk, M. A. Nichols, M. Okan, T. Gersdorf, V. V. Ramasesh, W. S. Bakr, T. Lompe, and M. W. Zwierlein, Phys. Rev. Lett.114, 193001 (2015)

work page 2015
[37]

Hartke, B

T. Hartke, B. Oreg, N. Jia, and M. Zwierlein, Nature 601, 537 (2022)

work page 2022
[38]

M. A. Nichols, L. W. Cheuk, M. Okan, T. R. Hartke, E. Mendez, T. Senthil, E. Khatami, H. Zhang, and M. W. Zwierlein, Science363, 383 (2019)

work page 2019
[39]

Zhou and T.-L

Q. Zhou and T.-L. Ho, Phys. Rev. Lett.106, 225301 (2011). 6 SUPPLEMENT AR Y INFORMA TION A. Experimental setup The attractive Fermi-Hubbard model is realized from a degenerate gas comprised of the two lowest hyperfine states of 40K:|F= 9/2, m F =−9/2⟩and|F= 9/2, m F =−7/2⟩. The atoms occupy a single two-dimensional plane of a three-dimensional optical lat...

work page 2011