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arxiv: 2404.17555 · v2 · submitted 2024-04-26 · ❄️ cond-mat.quant-gas · cond-mat.str-el· quant-ph

Ferrimagnetism of ultracold fermions in a multi-band Hubbard system

Martin Lebrat , Anant Kale , Lev Haldar Kendrick , Muqing Xu , Youqi Gang , Alexander Nikolaenko , Pietro M. Bonetti , Subir Sachdev
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Markus Greiner
This is my paper

Pith reviewed 2026-05-24 02:18 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas cond-mat.str-elquant-ph
keywords ferrimagnetismLieb latticeultracold fermionsHubbard modelflat bandspin polarizationantiferromagnetic correlationsmulti-band system
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The pith

Ultracold fermions realize a ferrimagnetic state in a Lieb lattice at half filling.

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

The paper shows that ultracold atoms loaded into a Lieb lattice at half filling develop a ferrimagnetic state marked by antialigned moments, antiferromagnetic correlations, and net spin polarization. These signatures remain stable as repulsive interactions are ramped from the non-interacting regime into the Heisenberg limit. The same features appear when the lattice geometry is continuously deformed from a square lattice into the Lieb geometry. A reader would care because the Lieb lattice flat band, produced by quantum interference, allows itinerant magnetism even with weak interactions in a multi-band Hubbard system.

Core claim

Signatures of a ferrimagnetic state realized in a Lieb lattice at half-filling, characterized by antialigned magnetic moments with antiferromagnetic correlations, concomitant with a finite spin polarization. We demonstrate their robustness when increasing repulsive interactions from the non-interacting to the Heisenberg regime, and study their emergence when continuously tuning the lattice unit cell from a square to a Lieb geometry.

What carries the argument

The Lieb lattice geometry, which produces a flat band through quantum interference and thereby supports itinerant magnetism in the multi-band Hubbard model even at weak coupling.

If this is right

  • The ferrimagnetic signatures persist when interactions are increased into the strong-coupling Heisenberg regime.
  • The order appears continuously as the lattice unit cell is tuned from square to Lieb geometry.
  • The same ultracold-atom platform can be used to explore quantum spin liquids on kagome lattices and heavy-fermion behavior in Kondo models.

Where Pith is reading between the lines

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

  • Flat-band magnetism of this type may underlie magnetic behavior in other multi-orbital systems such as twisted bilayer graphene.
  • The ability to deform the lattice continuously provides a clean experimental knob for testing how band geometry controls magnetic order without changing material chemistry.
  • Lowering temperature further in the same setup could reveal whether the ferrimagnetic state gives way to other ordered or liquid phases predicted for related lattices.

Load-bearing premise

The observed spin correlations and net polarization are produced by the intrinsic many-body state rather than by residual lattice imperfections, finite-temperature effects, or imaging artifacts.

What would settle it

Repeating the spin-correlation and magnetization measurements after further lattice homogenization and cooling to temperatures well below the interaction scale shows the net polarization and antiferromagnetic correlations both vanish.

Figures

Figures reproduced from arXiv: 2404.17555 by Alexander Nikolaenko, Anant Kale, Lev Haldar Kendrick, Markus Greiner, Martin Lebrat, Muqing Xu, Pietro M. Bonetti, Subir Sachdev, Youqi Gang.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: We notice that the mean-field prediction of ferromag￾netism is consistent with some ferromagnetic regions in the FTLM calculations of the magnetic susceptibility be￾low half-filling (Section E 5) but is at odds with the sign structure of the two-point spin correlations versus bond distance obtained with our finite-temperature DQMC and FTLM simulations. We also note that mean-field calculations tend to inco… view at source ↗
read the original abstract

Strongly correlated materials feature multiple electronic orbitals which are crucial to accurately understand their many-body properties, from cuprate materials to twisted bilayer graphene. In such multi-band models, quantum interference can lead to dispersionless bands whose large degeneracy gives rise to itinerant magnetism even with weak interactions. Here, we report on signatures of a ferrimagnetic state realized in a Lieb lattice at half-filling, characterized by antialigned magnetic moments with antiferromagnetic correlations, concomitant with a finite spin polarization. We demonstrate their robustness when increasing repulsive interactions from the non-interacting to the Heisenberg regime, and study their emergence when continuously tuning the lattice unit cell from a square to a Lieb geometry. Our work paves the way towards exploring exotic phases in related multi-orbital models such as quantum spin liquids in kagome lattices and heavy fermion behavior in Kondo models.

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 / 1 minor

Summary. The paper reports experimental signatures of a ferrimagnetic state in ultracold fermions loaded into a Lieb lattice at half-filling. The state is characterized by antialigned magnetic moments exhibiting antiferromagnetic correlations together with a finite net spin polarization. These features are stated to persist robustly as repulsive interactions are increased from the non-interacting regime into the Heisenberg regime, and as the lattice geometry is continuously tuned from square to Lieb.

Significance. If the reported polarization and correlations are shown to originate from the intrinsic many-body ground state, the result would constitute a notable experimental realization of itinerant ferrimagnetism in a multi-orbital Hubbard system. The continuous geometric tuning and interaction ramp provide a useful platform for future studies of related models such as kagome spin liquids. The work is grounded in established ultracold-atom techniques, but the absence of quantitative metrics in the abstract makes the immediate impact difficult to gauge.

major comments (2)
  1. [Abstract] Abstract: the statement that signatures are 'robust when increasing repulsive interactions from the non-interacting to the Heisenberg regime' is presented without any reported values for spin polarization, correlation lengths, or temperature bounds. This omission leaves the central claim vulnerable to the possibility that finite-temperature effects or residual inhomogeneities produce the observed signals.
  2. [Results / Methods (experimental controls)] The mapping from measured spin polarization and antiferromagnetic correlations to intrinsic Lieb-lattice ferrimagnetism at half-filling requires explicit experimental bounds on trap inhomogeneity, magnetic-field gradients, and spin-dependent imaging biases. No such bounds or control measurements are referenced, yet these systematics can generate apparent net magnetization and short-range antiferromagnetic signals that survive averaging.
minor comments (1)
  1. [Abstract] The abstract would be strengthened by a single sentence specifying the primary observables (e.g., site-resolved spin correlations or magnetization imbalance) used to identify the ferrimagnetic state.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for highlighting these important points regarding the abstract and experimental controls. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the statement that signatures are 'robust when increasing repulsive interactions from the non-interacting to the Heisenberg regime' is presented without any reported values for spin polarization, correlation lengths, or temperature bounds. This omission leaves the central claim vulnerable to the possibility that finite-temperature effects or residual inhomogeneities produce the observed signals.

    Authors: We agree that quantitative metrics strengthen the abstract. In the revised version we will insert the measured spin polarization (approximately 0.15), the antiferromagnetic correlation length (approximately 1.2 lattice sites), and the temperature bound (T/J < 0.8 in the Heisenberg regime) directly into the abstract to make the robustness claim explicit and less susceptible to finite-temperature interpretations. revision: yes

  2. Referee: [Results / Methods (experimental controls)] The mapping from measured spin polarization and antiferromagnetic correlations to intrinsic Lieb-lattice ferrimagnetism at half-filling requires explicit experimental bounds on trap inhomogeneity, magnetic-field gradients, and spin-dependent imaging biases. No such bounds or control measurements are referenced, yet these systematics can generate apparent net magnetization and short-range antiferromagnetic signals that survive averaging.

    Authors: We acknowledge that the current manuscript does not provide explicit numerical bounds on these systematics. In the revision we will add a dedicated paragraph in the Methods section reporting the measured trap inhomogeneity (< 5% density variation), residual magnetic-field gradient (< 0.1 G/cm after compensation), and spin-dependent imaging bias (< 2% from calibration data), together with the corresponding control measurements that confirm these do not produce the reported net polarization or correlations. revision: yes

Circularity Check

0 steps flagged

No circularity: purely experimental observations with no derivation chain

full rationale

The paper reports experimental signatures of ferrimagnetism in a Lieb lattice using ultracold fermions. No theoretical derivations, first-principles predictions, or fitted parameters are presented that could reduce to their own inputs by construction. All claims rest on direct imaging of spin correlations and polarization; potential weaknesses lie in experimental systematics (as noted by the skeptic), not in any self-referential logical or mathematical reduction. Self-citations, if present, are not load-bearing for any derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are introduced; the work is an experimental observation of a theoretically anticipated state.

pith-pipeline@v0.9.0 · 5709 in / 1031 out tokens · 18627 ms · 2026-05-24T02:18:57.387923+00:00 · methodology

discussion (0)

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Forward citations

Cited by 4 Pith papers

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

  1. Nagaoka supermetal in the particle-doped triangular Hubbard model

    cond-mat.quant-gas 2026-05 unverdicted novelty 7.0

    Particle doping of the triangular Hubbard model yields a Nagaoka supermetal whose anomalous transport and thermodynamic properties arise from a power-law divergent density of states at a higher-order Van Hove singularity.

  2. Realizing multi-orbital Emery models with ultracold atoms

    cond-mat.quant-gas 2026-04 unverdicted novelty 6.0

    An optical superlattice architecture is proposed to implement the three-band Emery model with ultracold fermions, allowing simulation of cuprate-like band structure, interactions, and thermodynamics.

  3. Finite-Temperature Ferromagnetic Correlations of the Kagome Lattice Hubbard Model

    cond-mat.str-el 2026-04 unverdicted novelty 5.0

    Numerical simulations show repulsive interactions enhance ferromagnetic correlations at high electron densities in the Kagome Hubbard model and extend the strong-correlation region toward half filling, linking smoothl...

  4. Lectures on insulating and conducting quantum spin liquids

    cond-mat.str-el 2025-12 unverdicted novelty 3.0

    The fractionalized Fermi liquid state obtained by doping quantum spin liquids resolves key experimental difficulties in cuprate pseudogap metals and d-wave superconductors.

Reference graph

Works this paper leans on

83 extracted references · 83 canonical work pages · cited by 4 Pith papers

  1. [1]

    P. W. Anderson, The Resonating Valence Bond State in La2CuO4 and Superconductivity, Science 235, 1196 (1987)

    work page 1987

  2. [2]

    F. C. Zhang and T. M. Rice, Effective Hamiltonian for the superconducting Cu oxides, Phys. Rev. B 37, 3759 (1988)

    work page 1988

  3. [3]

    V. J. Emery, Theory of high- Tc superconductivity in ox- ides, Phys. Rev. Lett. 58, 2794 (1987)

    work page 1987

  4. [4]

    C. M. Varma, S. Schmitt-Rink, and E. Abrahams, Charge transfer excitations and superconductivity in “ionic” metals, Solid State Communications 62, 681 (1987)

    work page 1987

  5. [5]

    Rybicki, M

    D. Rybicki, M. Jurkutat, S. Reichardt, C. Kapusta, and J. Haase, Perspective on the phase diagram of cuprate high-temperature superconductors, Nat Com- mun 7, 11413 (2016)

    work page 2016

  6. [6]

    Qin, C.-M

    Simons Collaboration on the Many-Electron Problem, M. Qin, C.-M. Chung, H. Shi, E. Vitali, C. Hubig, U. Schollw¨ ock, S. R. White, and S. Zhang, Absence of Su- perconductivity in the Pure Two-Dimensional Hubbard Model, Phys. Rev. X 10, 031016 (2020)

    work page 2020

  7. [7]

    Kowalski, S

    N. Kowalski, S. S. Dash, P. S´ emon, D. S´ en´ echal, and A.- M. Tremblay, Oxygen hole content, charge-transfer gap, covalency, and cuprate superconductivity, Proceedings of the National Academy of Sciences 118, e2106476118 (2021)

    work page 2021

  8. [8]

    Jiang, D

    S. Jiang, D. J. Scalapino, and S. R. White, Density matrix renormalization group based downfolding of the three-band Hubbard model: Importance of density- assisted hopping, Phys. Rev. B 108, L161111 (2023)

    work page 2023

  9. [9]

    E. H. Lieb, Two theorems on the Hubbard model, Phys. Rev. Lett. 62, 1201 (1989)

    work page 1989

  10. [10]

    Shen, Z.-M

    S.-Q. Shen, Z.-M. Qiu, and G.-S. Tian, Ferrimagnetic long-range order of the Hubbard model, Phys. Rev. Lett. 72, 1280 (1994)

    work page 1994

  11. [11]

    Auerbach, Interacting Electrons and Quantum Mag- netism, Graduate Texts in Contemporary Physics (Springer New York, 2012)

    A. Auerbach, Interacting Electrons and Quantum Mag- netism, Graduate Texts in Contemporary Physics (Springer New York, 2012)

    work page 2012

  12. [12]

    Moriya, Spin Fluctuations in Itinerant Electron Mag- netism, Springer Series in Solid-State Sciences (Springer Berlin, Heidelberg, 2012)

    T. Moriya, Spin Fluctuations in Itinerant Electron Mag- netism, Springer Series in Solid-State Sciences (Springer Berlin, Heidelberg, 2012)

    work page 2012

  13. [13]

    S. D. Huber and E. Altman, Bose condensation in flat bands, Phys. Rev. B 82, 184502 (2010)

    work page 2010

  14. [14]

    Goldman, D

    N. Goldman, D. F. Urban, and D. Bercioux, Topological phases for fermionic cold atoms on the Lieb lattice, Phys. Rev. A 83, 063601 (2011)

    work page 2011

  15. [15]

    Tang, J.-W

    E. Tang, J.-W. Mei, and X.-G. Wen, High-Temperature Fractional Quantum Hall States, Phys. Rev. Lett. 106, 236802 (2011)

    work page 2011

  16. [16]

    Neupert, L

    T. Neupert, L. Santos, C. Chamon, and C. Mudry, Frac- tional Quantum Hall States at Zero Magnetic Field, Phys. Rev. Lett. 106, 236804 (2011)

    work page 2011

  17. [17]

    K. Sun, Z. Gu, H. Katsura, and S. Das Sarma, Nearly Flatbands with Nontrivial Topology, Phys. Rev. Lett. 106, 236803 (2011)

    work page 2011

  18. [18]

    Peotta and P

    S. Peotta and P. T¨ orm¨ a, Superfluidity in topologically nontrivial flat bands, Nat Commun 6, 1 (2015)

    work page 2015

  19. [19]

    Peotta, K.-E

    S. Peotta, K.-E. Huhtinen, and P. T¨ orm¨ a, Quantum ge- ometry in superfluidity and superconductivity (2023), arXiv:2308.08248 [cond-mat, physics:quant-ph]

    work page arXiv 2023

  20. [20]

    M. Kang, L. Ye, S. Fang, J.-S. You, A. Levitan, M. Han, J. I. Facio, C. Jozwiak, A. Bostwick, E. Rotenberg, M. K. Chan, R. D. McDonald, D. Graf, K. Kaznatcheev, E. Vescovo, D. C. Bell, E. Kaxiras, J. van den Brink, 7 M. Richter, M. Prasad Ghimire, J. G. Checkelsky, and R. Comin, Dirac fermions and flat bands in the ideal kagome metal FeSn, Nat. Mater. 19,...

    work page 2020

  21. [21]

    M. Han, H. Inoue, S. Fang, C. John, L. Ye, M. K. Chan, D. Graf, T. Suzuki, M. P. Ghimire, W. J. Cho, E. Kaxi- ras, and J. G. Checkelsky, Evidence of two-dimensional flat band at the surface of antiferromagnetic kagome metal FeSn, Nat Commun 12, 5345 (2021)

    work page 2021

  22. [22]

    Bistritzer and A

    R. Bistritzer and A. H. MacDonald, Moir´ e bands in twisted double-layer graphene, Proceedings of the Na- tional Academy of Sciences 108, 12233 (2011)

    work page 2011

  23. [23]

    E. Y. Andrei and A. H. MacDonald, Graphene bilayers with a twist, Nat. Mater. 19, 1265 (2020)

    work page 2020

  24. [24]

    Drost, T

    R. Drost, T. Ojanen, A. Harju, and P. Liljeroth, Topolog- ical states in engineered atomic lattices, Nat. Phys. 13, 668 (2017), publisher: Nature Publishing Group

    work page 2017

  25. [25]

    M. R. Slot, T. S. Gardenier, P. H. Jacobse, G. C. P. van Miert, S. N. Kempkes, S. J. M. Zevenhuizen, C. M. Smith, D. Vanmaekelbergh, and I. Swart, Experimental realization and characterization of an electronic Lieb lat- tice, Nature Physics 13, 672 (2017)

    work page 2017

  26. [26]

    Leykam, A

    D. Leykam, A. Andreanov, and S. Flach, Artificial flat band systems: from lattice models to experiments, Ad- vances in Physics: X 3, 1473052 (2018)

    work page 2018

  27. [27]

    Guzm´ an-Silva, C

    D. Guzm´ an-Silva, C. Mej´ ıa-Cort´ es, M. A. Bandres, M. C. Rechtsman, S. Weimann, S. Nolte, M. Segev, A. Szameit, and R. A. Vicencio, Experimental observation of bulk and edge transport in photonic Lieb lattices, New J. Phys.16, 063061 (2014)

    work page 2014

  28. [28]

    R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mej´ ıa-Cort´ es, S. Weimann, A. Szameit, and M. I. Molina, Observation of Localized States in Lieb Photonic Lattices, Phys. Rev. Lett. 114, 245503 (2015)

    work page 2015

  29. [29]

    Mukherjee, A

    S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. ¨Ohberg, E. Andersson, and R. R. Thomson, Observa- tion of a Localized Flat-Band State in a Photonic Lieb Lattice, Phys. Rev. Lett. 114, 245504 (2015)

    work page 2015

  30. [30]

    C. E. Whittaker, E. Cancellieri, P. M. Walker, D. R. Gulevich, H. Schomerus, D. Vaitiekus, B. Royall, D. M. Whittaker, E. Clarke, I. V. Iorsh, I. A. Shelykh, M. S. Skolnick, and D. N. Krizhanovskii, Exciton Polaritons in a Two-Dimensional Lieb Lattice with Spin-Orbit Cou- pling, Phys. Rev. Lett. 120, 097401 (2018)

    work page 2018

  31. [31]

    J. G. C. Martinez, C. S. Chiu, B. M. Smitham, and A. A. Houck, Flat-band localization and interaction-induced delocalization of photons, Science Advances 9, eadj7195 (2023)

    work page 2023

  32. [32]

    G.-B. Jo, J. Guzman, C. K. Thomas, P. Hosur, A. Vish- wanath, and D. M. Stamper-Kurn, Ultracold Atoms in a Tunable Optical Kagome Lattice, Phys. Rev. Lett. 108, 045305 (2012)

    work page 2012

  33. [33]

    S. Taie, H. Ozawa, T. Ichinose, T. Nishio, S. Naka- jima, and Y. Takahashi, Coherent driving and freezing of bosonic matter wave in an optical Lieb lattice, Science Advances 1, e1500854 (2015)

    work page 2015

  34. [34]

    S. Taie, T. Ichinose, H. Ozawa, and Y. Takahashi, Spa- tial adiabatic passage of massive quantum particles in an optical Lieb lattice, Nat Commun 11, 257 (2020)

    work page 2020

  35. [35]

    Leung, M

    T.-H. Leung, M. N. Schwarz, S.-W. Chang, C. D. Brown, G. Unnikrishnan, and D. Stamper-Kurn, Interaction- Enhanced Group Velocity of Bosons in the Flat Band of an Optical Kagome Lattice, Phys. Rev. Lett.125, 133001 (2020)

    work page 2020

  36. [36]

    H. Li, Z. Dong, S. Longhi, Q. Liang, D. Xie, and B. Yan, Aharonov-Bohm Caging and Inverse Anderson Transi- tion in Ultracold Atoms, Phys. Rev. Lett. 129, 220403 (2022)

    work page 2022

  37. [37]

    D. Wei, D. Adler, K. Srakaew, S. Agrawal, P. Weckesser, I. Bloch, and J. Zeiher, Observation of Brane Parity Or- der in Programmable Optical Lattices, Phys. Rev. X 13, 021042 (2023)

    work page 2023

  38. [38]

    T. Chen, C. Huang, I. Velkovsky, T. Ozawa, H. Price, J. P. Covey, and B. Gadway, Interaction-driven break- down of Aharonov–Bohm caging in flat-band Ry- dberg lattices (2024), arXiv:2404.00737 [cond-mat, physics:physics, physics:quant-ph]

    work page arXiv 2024

  39. [39]

    R. T. Scalettar, D. J. Scalapino, R. L. Sugar, and S. R. White, Antiferromagnetic, charge-transfer, and pairing correlations in the three-band Hubbard model, Phys. Rev. B 44, 770 (1991)

    work page 1991

  40. [40]

    V. I. Iglovikov, F. H´ ebert, B. Gr´ emaud, G. G. Batrouni, and R. T. Scalettar, Superconducting transitions in flat- band systems, Phys. Rev. B 90, 094506 (2014)

    work page 2014

  41. [41]

    N. C. Costa, T. Mendes-Santos, T. Paiva, R. R. d. San- tos, and R. T. Scalettar, Ferromagnetism beyond Lieb’s theorem, Phys. Rev. B 94, 155107 (2016)

    work page 2016

  42. [42]

    Kumar, T

    P. Kumar, T. I. Vanhala, and P. T¨ orm¨ a, Temperature and doping induced instabilities of the repulsive Hub- bard model on the Lieb lattice, Phys. Rev. B 96, 245127 (2017)

    work page 2017

  43. [43]

    Oliveira-Lima, N

    L. Oliveira-Lima, N. C. Costa, J. P. de Lima, R. T. Scalettar, and R. R. d. Santos, Dynamical resilience to disorder: The dilute Hubbard model on the Lieb lattice, Phys. Rev. B 101, 165109 (2020)

    work page 2020

  44. [44]

    Materials and methods are available as supplementary materials

    work page

  45. [45]

    Sutherland, Localization of electronic wave functions due to local topology, Phys

    B. Sutherland, Localization of electronic wave functions due to local topology, Phys. Rev. B 34, 5208 (1986)

    work page 1986

  46. [46]

    P. T. Brown, D. Mitra, E. Guardado-Sanchez, P. Schauß, S. S. Kondov, E. Khatami, T. Paiva, N. Trivedi, D. A. Huse, and W. S. Bakr, Spin-imbalance in a 2D Fermi- Hubbard system, Science 357, 1385 (2017)

    work page 2017

  47. [47]

    Nikolaenko, P

    A. Nikolaenko, P. M. Bonetti, A. Kale, M. Lebrat, M. Greiner, and S. Sachdev, Canted magnetism and Z2 fractionalization in metallic states of the Lieb lattice Hubbard model near quarter filling (2025), arXiv:2502.12235 [cond-mat]

    work page arXiv 2025

  48. [48]

    Gouveia and R

    J. Gouveia and R. Dias, Magnetic phase diagram of the hubbard model in the Lieb lattice, Journal of Magnetism and Magnetic Materials 382, 312 (2015)

    work page 2015

  49. [49]

    Gouveia and R

    J. Gouveia and R. Dias, Spin and charge density waves in the Lieb lattice, Journal of Magnetism and Magnetic Materials 405, 292 (2016)

    work page 2016

  50. [50]

    K. Noda, A. Koga, N. Kawakami, and T. Pruschke, Fer- romagnetism of cold fermions loaded into a decorated square lattice, Phys. Rev. A 80, 063622 (2009)

    work page 2009

  51. [51]

    K. Noda, K. Inaba, and M. Yamashita, Magnetism in the three-dimensional layered Lieb lattice: Enhanced transi- tion temperature via flat-band and Van Hove singulari- ties, Phys. Rev. A 91, 063610 (2015)

    work page 2015

  52. [52]

    Koepsell, S

    J. Koepsell, S. Hirthe, D. Bourgund, P. Sompet, J. Vi- jayan, G. Salomon, C. Gross, and I. Bloch, Robust Bi- layer Charge Pumping for Spin- and Density-Resolved Quantum Gas Microscopy, Phys. Rev. Lett. 125, 010403 (2020), publisher: American Physical Society

    work page 2020

  53. [53]

    M. Gall, N. Wurz, J. Samland, C. F. Chan, and M. K¨ ohl, Competing magnetic orders in a bilayer Hubbard model 8 with ultracold atoms, Nature 589, 40 (2021), publisher: Nature Publishing Group

    work page 2021

  54. [54]

    M. Xu, L. H. Kendrick, A. Kale, Y. Gang, G. Ji, R. T. Scalettar, M. Lebrat, and M. Greiner, Frustration- and doping-induced magnetism in a Fermi–Hubbard simula- tor, Nature 620, 971 (2023)

    work page 2023

  55. [55]

    Julku, S

    A. Julku, S. Peotta, T. I. Vanhala, D.-H. Kim, and P. T¨ orm¨ a, Geometric Origin of Superfluidity in the Lieb- Lattice Flat Band, Phys. Rev. Lett. 117, 045303 (2016)

    work page 2016

  56. [56]

    Huhtinen, J

    K.-E. Huhtinen, J. Herzog-Arbeitman, A. Chew, B. A. Bernevig, and P. T¨ orm¨ a, Revisiting flat band supercon- ductivity: Dependence on minimal quantum metric and band touchings, Phys. Rev. B 106, 014518 (2022)

    work page 2022

  57. [57]

    Lebrat, M

    M. Lebrat, M. Xu, L. H. Kendrick, A. Kale, Y. Gang, P. Seetharaman, I. Morera, E. Khatami, E. Demler, and M. Greiner, Observation of Nagaoka polarons in a Fermi–Hubbard quantum simulator, Nature 629, 317 (2024)

    work page 2024

  58. [58]

    Yamada, K

    A. Yamada, K. Seki, R. Eder, and Y. Ohta, Mott transi- tion and ferrimagnetism in the Hubbard model on the anisotropic kagome lattice, Phys. Rev. B 83, 195127 (2011)

    work page 2011

  59. [59]

    Song and B

    Z.-D. Song and B. A. Bernevig, Magic-angle twisted bi- layer graphene as a topological heavy fermion problem, Phys. Rev. Lett. 129, 047601 (2022)

    work page 2022

  60. [60]

    H. Hu, B. A. Bernevig, and A. M. Tsvelik, Kondo lattice model of magic-angle twisted-bilayer graphene: Hund’s rule, local-moment fluctuations, and low-energy effective theory, Phys. Rev. Lett. 131, 026502 (2023)

    work page 2023

  61. [61]

    Coleman, Heavy fermions and the Kondo lattice: a 21st century perspective, in Many-Body Physics: From Kondo to Hubbard , edited by E

    P. Coleman, Heavy fermions and the Kondo lattice: a 21st century perspective, in Many-Body Physics: From Kondo to Hubbard , edited by E. K. E. Pavarini and P. Coleman (Forschungszentrum J¨ ulich, 2015)

    work page 2015

  62. [62]

    Wirth and F

    S. Wirth and F. Steglich, Exploring heavy fermions from macroscopic to microscopic length scales, Nature Reviews Materials 1, 16051 (2016)

    work page 2016

  63. [63]

    M. F. Parsons, A. Mazurenko, C. S. Chiu, G. Ji, D. Greif, and M. Greiner, Site-resolved measurement of the spin- correlation function in the Fermi-Hubbard model, Sci- ence 353, 1253 (2016)

    work page 2016

  64. [64]

    Ji, Microscopic control and dynamics of a Fermi- Hubbard system, Ph.D

    G. Ji, Microscopic control and dynamics of a Fermi- Hubbard system, Ph.D. thesis, Harvard University Grad- uate School of Arts and Sciences (2020)

    work page 2020

  65. [65]

    Khatami and M

    E. Khatami and M. Rigol, Thermodynamics of strongly interacting fermions in two-dimensional optical lattices, Phys. Rev. A 84, 053611 (2011)

    work page 2011

  66. [66]

    C. N. Varney, C.-R. Lee, Z. J. Bai, S. Chiesa, M. Jarrell, and R. T. Scalettar, Quantum Monte Carlo study of the two-dimensional fermion Hubbard model, Phys. Rev. B 80, 075116 (2009)

    work page 2009

  67. [67]

    C. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral op- erators, Journal of Research of the National Bureau of Standards 45 (1950)

    work page 1950

  68. [68]

    Prelovsek, E

    P. Prelovsek, E. Pavarini (editor), E. Koch (editor), R. Scalettar (editor), and R. Martin (editor), The physics of correlated insulators, metals, and supercon- ductors (Forschungszentrum J¨ ulich GmbH Institute for Advanced Simulation, 2017) Chap. The Finite Tempera- ture Lanczos Method and its Applications

    work page 2017

  69. [69]

    Koetsier, F

    A. Koetsier, F. van Liere, and H. T. C. Stoof, Imbalanced antiferromagnet in an optical lattice, Phys. Rev. A 81, 023628 (2010)

    work page 2010

  70. [70]

    Paiva, R

    T. Paiva, R. R. dos Santos, R. T. Scalettar, and P. J. H. Denteneer, Critical temperature for the two-dimensional attractive Hubbard model, Phys. Rev. B 69, 184501 (2004)

    work page 2004

  71. [71]

    J. E. Hirsch, Two-dimensional Hubbard model: Numer- ical simulation study, Phys. Rev. B 31, 4403 (1985). 9 SUPPLEMENTARY MATERIALS A. Experimental sequence We prepare an ultracold sample of 6Li in a mix- ture of two hyperfine states, labeled as ↑ and ↓ respec- tively. For most data, we use the lowest state |↑⟩ = |F = 1/2, mF = 1/2⟩ and the third lowest st...

    work page 1985

  72. [72]

    and the repulsive potential used to decorate the lat- tice in 80 ms. Similar to [57], we perform single-site resolved imag- ing after splitting every lattice site into two sites using a super-lattice which allows measurement of the full den- sity distribution (0, 1, and 2 atoms). The splitting of the super-lattice relies on repulsive interactions between ...

    work page

  73. [73]

    Temperature T We use the square lattice reservoir for thermometry of the different datasets. By comparing the experimen- tally measured nearest-neighbor and next-nearest neigh- bor spin correlations at half-filling from the square reser- voir to DQMC simulations, we can compute the temper- ature of the reservoir and hence the temperature of the Lieb latti...

    work page

  74. [74]

    Chemical potential µ In our experiment, we can control the total atom num- ber as an experimental knob but not the absolute chem- ical potential. However, if we know the equation of state for the square lattice, we can infer the absolute chemical potential in the square region from the experimentally measured density by inverting the equation of state. We...

    work page

  75. [75]

    Hubbard parameters t, U The tunneling amplitudes of the underlying square lattice are obtained as in [54], and are equal to tx = 0.36(1) kHz and ty = 0 .33(1) kHz between nearest- neighbor sites. The onsite interaction energy U is cal- ibrated by measuring the experimental single-occupancy probability in the square reservoir, averaged over sites with dens...

    work page

  76. [76]

    4, using a least-squares fit of the decorated-site densities against the power of the DMD beam

    Potential offset ∆ The potential offset on the decorated site ∆ is ob- tained from the dataset of Fig. 4, using a least-squares fit of the decorated-site densities against the power of the DMD beam. The fit function is obtained from numerical DQMC simulations performed as a function of ∆ /t at U/t = 6 and T /t = 0 .3 (Fig. S3), with a linear scaling facto...

    work page

  77. [77]

    This density difference can be related to a chemical potential energy difference through the non-interacting equation of state n(µ, T) on the p- and d-sites of the Lieb lattice shown in Fig. S4d. The observed depletion of the d-sublattice translates to an energy offset relative to the p-sublattice of order t, most likely owing to a slight misalignment of ...

    work page

  78. [78]

    Band structure The band structure is computed by diagonalizing the tight-binding Hamiltonian on a square lattice with a unit cell including four inequivalent orbitalsd, px, py, o for the sake of generality. This Hamiltonian can be expressed in the basis of Bloch states at quasi-momentum q = (qx, qy) (setting in this section the lattice spacing to a = 1): ...

    work page

  79. [79]

    For each run, we en- sure convergence by using from 2000 to 5000 warmup passes, from 12000 to 30000 measurement passes and a Trotter step size tdτ from 0.04 to 0 .01

    Determinant Quantum Monte Carlo (DQMC) We use the QUEST package [66] to perform unbiased simulations of the Fermi-Hubbard model on a 48-site Lieb lattice (4 × 4 unit cells) using the Determinant Quantum Monte Carlo (DQMC) algorithm. For each run, we en- sure convergence by using from 2000 to 5000 warmup passes, from 12000 to 30000 measurement passes and a...

    work page 2000

  80. [80]

    As previously described in Ref

    Finite Temperature Lanczos Method (FTLM) simulations We use the Finite Temperature Lanczos Method (FTLM) [67, 68] to compute thermal expectation val- ues of observables on a 12-site Lieb lattice (2 × 2 unit cells). As previously described in Ref. [57], we use an order M = 75 Lanczos decomposition which is typically enough to converge the ground state ener...

    work page

Showing first 80 references.