Pith. sign in

REVIEW 3 major objections 7 minor 91 references

Shaping Magnetic Order by Local Frustration for Itinerant Fermions on a Graph

T0 review · 3 major / 7 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Local frustration centers bind singlets while sharing a delocalized hole, so embedding diagonals lowers the ground-state spin by about one per bond.

desk verdict A credible, reproducible numerical study of kinetic magnetism on frustrated graphs; the headline 'general principle' is extrapolated beyond the finite-size evidence, but the core observations are solid and deserve referee time. read the letter →

arxiv 2507.07886 v2 pith:GAEOSPDI submitted 2025-07-10 cond-mat.str-el cond-mat.dis-nncond-mat.quant-gascond-mat.stat-mech

Revathy B S , Shovan Dutta This is my paper · ORCID
classification cond-mat.str-elcond-mat.dis-nncond-mat.quant-gascond-mat.stat-mech
keywords kineticmagnetismHubbardmodelNagaokaferromagnetismgeometricfrustrationsingletbindingrandomgraphsShastry-Sutherlandlatticecold-atomquantumsimulation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish a general principle for kinetic magnetism, the magnetism generated by a hole moving through strongly interacting fermions: a local frustration center, such as an odd loop or an added diagonal bond, binds one singlet while the same hole stays delocalized and the remaining spins stay aligned. If the principle is right, the magnetic order of a strongly correlated system can be shaped by editing the graph rather than by tuning exchange couplings. On a rectangular grid, each added diagonal bond lowers the ground-state total spin by roughly one. On random graphs, the total spin is anticorrelated with the number of odd loops and with the frustration index, and it oscillates with the smallest loop size. None of this happens for exchange magnetism at half filling.

What carries the argument

The central object is the one-hole, $U\to\infty$ Hubbard model on a graph, whose low-energy physics is governed entirely by the hole's hopping while double occupancy is forbidden. The load-bearing mechanism is the frustration center, meaning a diagonal bond or odd loop that spoils the constructive interference behind the ferromagnetic ground state, binding exactly one singlet while the same hole is shared across the graph. The paper analyzes this with exact diagonalization of the combined hole-and-magnon Hilbert space, builds variational cross-dimer states for collective plaquettes, and defines frustration measures such as the number of odd loops, the frustration index, and the minimum loop size to organize the random-graph results.

What would settle it

Compute the ground-state total spin of a much larger frustrated graph, such as a grid with dozens of random diagonal bonds or random graphs with hundreds of sites, by a scalable numerical method: if the average spin reduction per diagonal stops being roughly one, or if the hole's density localizes on the frustration centers, the general principle fails. A cold-atom experiment with two or three engineered diagonal bonds could also falsify it by measuring the total spin or spin correlations and finding a reduction different from one per bond.

Watch

Extended reading notes

Core claim

In the infinite-$U$ Hubbard model with a single hole, the paper claims that the ground state on a frustrated graph is organized by the rule that frustration centers bind singlets while sharing a delocalized hole. The hole's kinetic interference, which normally favors a fully aligned ferromagnet on bipartite lattices, is locally spoiled by an odd loop or a diagonal bond; that spoiled region traps a down spin into a singlet, while the hole keeps moving and the rest of the lattice stays spin-polarized. Consequently the ground-state total spin $S_{\rm total}$ drops by approximately one per added diagonal on a rectangular grid, and two nearby frustrated plaquettes can share the hole and bind distorted singlets collectively. On random graphs the same principle shows up statistically: $S_{\rm total}$ is anticorrelated with the frustration index and with odd-loop counts, positively correlated with even-loop counts, and its distribution swings as the minimum loop size is increased. The authors present this as a collective effect that exchange magnetism does not possess.

Load-bearing premise

The small-system numerical results, covering graphs with 20 sites, a 4-by-5 grid, and ladders up to 32 sites, are assumed to keep holding on arbitrarily large graphs, with every frustration center still binding exactly one singlet and the hole staying delocalized; the paper gives no proof or thermodynamic-limit scaling for that step.

Editorial extensions

If this is right

  • On a rectangular grid with one hole, adding a diagonal bond to a plaquette reduces the ground-state total spin by approximately one, so the net magnetization can be tuned in unit steps by embedding frustration centers.
  • On random graphs, ground-state total spin is strongly anticorrelated with the frustration index and with the number of odd loops, and positively correlated with even loops; restricting the minimum loop size swings the magnetization distribution between nearly ferromagnetic and nearly singlet.
  • Two frustrated plaquettes placed close together share the hole and bind distorted singlets collectively, producing regions where the spin reduction exceeds what independent plaquettes would give.
  • A focused-laser protocol can create effective diagonal hops in selected plaquettes of a cold-atom optical lattice, making the key predictions testable in existing experiments.
  • Exchange magnetism at half filling shows no such sensitivity to diagonal bonds or loop structure, so this effect is diagnostic of kinetic magnetism.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, the additivity of the spin reduction suggests that any set of well-separated frustration centers on a large graph should give a predictable saturation value of $S_{\rm total}$, turning the rule into a design recipe for synthetic quantum magnets.
  • Beyond the paper, if the principle survives the thermodynamic limit, standard network diagnostics such as odd-loop density, girth, and frustration index become direct predictors of a quantum ground-state property, connecting network science to strongly correlated electron physics.
  • Beyond the paper, one could test the hole-sharing claim directly by measuring the hole's inverse participation ratio on a large frustrated lattice: the principle predicts the hole remains delocalized even when all magnons are pinned to frustration centers.
  • Beyond the paper, multi-hole versions may inherit the same mechanism and produce interactions between singlet centers, since the shared hole mediates the collective binding seen in the two-plaquette calculation.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 7 minor

Summary. This paper studies how local kinetic frustration shapes magnetic order in the infinite-U Hubbard model with a single hole on a graph. The authors solve a single square with diagonal hopping exactly, identifying three regions: a Nagaoka ferromagnet, a vertical-singlet state, and a cross-dimer singlet, with an exact energy expression in the intermediate region. They then embed one or two frustrated plaquettes in ladders, using exact diagonalization and DMRG up to length 32, and show that the frustrated plaquette binds magnons with perturbatively controlled weights (P_out = 1/5 for the ladder, 1/9 for the grid). The central claim is a general principle: local frustration centers bind singlets while sharing a delocalized hole, so each added diagonal bond on a 4x5 grid reduces the ground-state total spin by roughly 1, and the total spin on 20-site random graphs is anticorrelated with loop counts and the frustration index. A half-filled Heisenberg comparison shows none of this sensitivity. An appendix outlines an optical-lattice scheme for realizing tunable diagonal hops.

Significance. Strengths: the single-square solution is exact and its three phases are characterized analytically with parity assignments; the perturbation-theory prediction for the magnon occupation outside the frustrated plaquette (P_out = 1/5) is verified against ED across the whole cross-dimer region; the ladder phase diagrams are stable to length 32 in DMRG; the Heisenberg contrast cleanly isolates the kinetic mechanism; and the data and source codes are archived on Zenodo (refs. 80-81). The most valuable outcome, if confirmed at larger size, is a falsifiable design rule: placing a diagonal bond in an otherwise bipartite ferromagnetic background locally binds a singlet and lowers S_total by one, enabling spatially resolved control of magnetization that exchange magnetism cannot provide. The variational ansatz for the two-plaquette collective state is presented with overlap data rather than as a derivation, and the fitted parameter alpha is not used as an input to the additivity claim, so no circularity is apparent.

major comments (3)
  1. [Grid with diagonal bonds (Fig. 4a)] The central additivity claim is not what Fig. 4(a) shows over its full range. For the 4x5 grid with 19 fermions, S_max = 9.5 and the hard lower bound is S = 1/2, so at most 9 of the 12 possible diagonals can reduce S by a full unit. The average total spin plotted in Fig. 4(a) falls from about 9.5 at N_diag = 0 to about 1.5 at N_diag = 12, i.e., an average reduction of roughly 8 units over 12 diagonals, or about 2/3 per diagonal, not 1. The paper does not state this saturation bound, does not identify the crossover where the slope-1 rule must fail, and does not report how the distribution over the 1000 graphs interacts with the S = 1/2 floor. In addition, the text claims that the Shastry-Sutherland-constrained placement reduces S by 1 per diagonal, but Fig. 4(a) shows the unconstrained case; the two should be shown separately, since the unconstrained data as plotted are consistent with a much weaker average slope near the upper end of N_diag. Because the headline general principle is exactly the additive slope-1 behavior, a quantitative regime statement, including the dependence on the diagonal-to-side hopping ratio (held fixed at t' = t in the grid data), is required.
  2. [Random graphs (Fig. 5; SM Fig. S5)] The extension to random graphs rests on exact diagonalization of 20-site graphs, with SM Fig. S5 extending the loop-count correlations down to 10 sites. This is encouraging but is not a scaling analysis: no statement is made about whether the about -0.5 correlation with the frustration index or the loop-count correlations converge with N, and the mechanism advanced for grids (each frustration center binds one singlet while the hole stays delocalized) is not directly testable on random graphs because, as the authors note, these do not have well-defined frustration centers. The abstract's claim that the principle extends to random graphs therefore currently bridges from a local mechanism to aggregate loop statistics by analogy. Either add a finite-size study showing a trend (e.g., correlation strength and S-distribution moments for N = 22-28 in fixed S_z sectors), or explicitly delimit the random-graph claim to what is computed.
  3. [Abstract and Figs. 3-4] The stated general principle, that local frustration centers bind singlets while sharing a delocalized hole, is not the operative mechanism in all regimes presented in the paper. In region V of Fig. 3 the hole is localized in one plaquette while the other stays polarized (S is still reduced by 2), and in region III the hole is confined between the plaquettes with two domain walls; a shared, delocalized hole occurs only in regions II and IV. Furthermore, all grid data in Fig. 4 are taken at one parameter point, equal hopping on all bonds, which for a single square sits exactly at the II-III degeneracy in Fig. 1(b); for a weaker diagonal (u < 1/5 in Fig. 1) a single square remains a fully polarized Nagaoka ferromagnet and the reduction per diagonal is zero, so the additivity rule must depend on the frustration strength and not just on the number of centers. The general principle should be reformulated with its regime of validity (hopping ratio, distance between centers, and proximity to saturation), or the claims should be explicitly presented as regime-specific.
minor comments (7)
  1. [Fig. 4 caption] Please clarify how the N_diag axis is sampled: are the plotted points independent random graphs with exactly N_diag diagonals, or averages over growth trajectories in which bonds are added one at a time? The two procedures give different distributions, and the caption's 'up to 1000 graphs' does not resolve this.
  2. [Appendix B / Fig. 8] The maximum variational overlap in region IV, |<psi(alpha*)|GS'>|^2 ~ 0.6-0.8, is moderate; the main text should state that the two-plaquette collective wavefunction is an illustration and that the primary evidence for region IV is the ED/DMRG reduction of S by 4.
  3. [Random graphs section] A Pearson correlation of about -0.5 is moderate, not 'strong' as stated in the text; please report the correlation type, the scatter, and confidence intervals (the SM already gives 95% intervals for Fig. S5), and soften the wording accordingly.
  4. [Fig. 3b] Please specify how the five regions of the two-plaquette phase diagram are delimited (e.g., level crossings between symmetry sectors) and whether the transitions are first-order; the figure currently shows no gap or transition data for this case.
  5. [Setup] The parenthetical comment '(For t_i,j < 0, ferromagnetism is not frustrated [36-38])' is too compressed; one sentence explaining the role of the hopping sign relative to the loop orientation would help readers who are not specialists in kinetic frustration.
  6. [SM Fig. S4] For the Heisenberg random-graph comparison, please report the fraction of nonseparable graphs in the ensembles that are non-bipartite and check the claim of 'negligible spread' of S around zero for r_min = 3, since an antiferromagnet on a graph containing an isolated odd cycle generically has a nonzero ground-state spin.
  7. [Appendix D] Please state the role of the central mediator site in the U to infinity limit: whether it is empty in the initial state, whether its on-site interaction enters the virtual tunneling, and what condition keeps it from being occupied; as written, the second-order process is described only through the band-structure plots in Fig. 10.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central singlet-binding principle is an independently computed result, not an input refit or a self-citation chain.

full rationale

The paper's central claim—that local frustration centers bind singlets while sharing a delocalized hole—is supported by several independent strands, none of which reduces to its own inputs. The single-square and single-plaquette results are exact or controlled: the ground-state sectors are obtained by direct diagonalization of the few-site Hubbard Hamiltonian, the large-u cross-dimer states are explicit wavefunctions with stated energies, and the leakage probabilities P_out = 1/5 (ladder) and 1/9 (grid) follow from an explicit third-order perturbation expansion in t/t'. These are parameter-free calculations, not fits. The grid and random-graph claims are numerical observations against exact diagonalization and DMRG benchmarks; the only fitted quantity, the variational deformation parameter alpha* in Appendix B, is chosen a posteriori to maximize overlap with the already-computed exact ground state and is not used to generate the S_total-reduction prediction. The frustration measures used for random graphs (odd/even loop counts, frustration index, bond-local loop counts) are independent graph-theoretic properties computed from the connectivity, while S_total and bond correlations are separately computed from the Hubbard Hamiltonian; the reported anticorrelations are empirical correlations, not definitional identities. The only self-reference is Ref. [33] (Preethi and Dutta), used for the exchange-magnetism comparison, but this is not load-bearing: the same comparison is independently reproduced in the Supplemental Material with HPhi exact diagonalization, and the kinetic-magnetism claims do not depend on that reference. The extrapolation from 20-site and 4x5 systems to arbitrarily large graphs is an untested finite-size assumption, which is a robustness and scaling concern rather than a circular reduction; within the sizes actually computed, the derivation is self-contained.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central claim is an empirical generalization from exact diagonalization and DMRG; the only fitted quantity in the paper is the variational deformation parameter alpha (approx 0.6), which is used to describe the two-plaquette collective state, not to derive the singlet-binding principle. Background assumptions are the standard U=infinity single-hole Hubbard limit and standard graph-theoretic definitions.

free parameters (1)
  • deformation parameter alpha = approx 0.6
    Variational parameter in Eqs. (2)-(3) tuned to maximize overlap with the ED ground state in region IV (Appendix B, Fig. 8). It characterizes distorted singlets but is not used to establish the central singlet-binding principle.
assumptions (5)
  • domain assumption U=infinity Hubbard model with exactly one hole
    The paper studies the limit of one hole and U to infinity so double occupancy is suppressed and only kinetic energy matters (Setup, Eq. (1)). This is the standard Nagaoka-type limit.
  • domain assumption Positive hopping amplitudes t>0 on all bonds
    The paper notes that for t<0 ferromagnetism is not frustrated (refs 36-38); the analysis assumes t>0 throughout.
  • standard math Ground-state total spin is well defined on nonseparable graphs
    Random-graph statistics restrict to nonseparable graphs so that S_total is unique in the ground state, citing Bobrow, Stubis and Li (ref 37).
  • domain assumption Heisenberg comparison at half filling uses J approx 4t^2/U
    To contrast with exchange magnetism, the SM maps the half-filled Hubbard model to an antiferromagnetic Heisenberg model with J approx 4t^2/U (SM Section I).
  • ad hoc to paper Variational product form for the two-plaquette collective state
    Eq. (2) assumes the ground state in region IV is of the form |psi(alpha)> = |x(alpha)> (x)_down + |x>_down (x(alpha)>, validated only by overlap with ED (Fig. 8), not derived.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Shaping Magnetic Order by Local Frustration for Itinerant Fermions on a Graph." pith.science (2026). https://pith.science/paper/GAEOSPDI

@misc{pith2026250707886,
  author       = {Pith},
  title        = {Pith review of: Shaping Magnetic Order by Local Frustration for Itinerant Fermions on a Graph},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GAEOSPDI}},
  note         = {Machine review of arXiv:2507.07886}
}
read the original abstract

Kinetic magnetism is an iconic and rare example of collective quantum order that emerges from the interference of paths taken by a hole in a sea of strongly interacting fermions. Here the lattice topology plays a fundamental role, with odd loops frustrating ferromagnetism, as seen in recent experiments. However, the resulting magnetic order on a general graph has remained elusive. Here we systematically establish a general principle: that local frustration centers bind singlets while sharing a delocalized hole. This collective effect -- absent in exchange magnetism -- extends from rectangular grids to random graphs, producing sharp and predictable variation with tunable frustration measures. Our findings demonstrate that one can shape the spin order and tune the net magnetization by embedding kinetic frustration, opening ways of spatially resolved quantum control of many-body systems. We outline a protocol to realize some of the key findings in existing cold-atom setups.

Figures

Figures reproduced from arXiv: 2507.07886 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Square with tunneling [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Ladder with a central frustrated plaquette. (b) [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Ladder with two frustrated plaquettes at a dis [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (5 more)
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Correlation between [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Reduction of total spin with the number of diago [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 8
Figure 8. Figure 8: FIG. 8. (a) Maximum overlap [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Correlation of (a) [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. (a) Square lattice (black dots) with a central site [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

91 extracted references · 56 canonical work pages

  1. [1]

    Lacroix, P

    C. Lacroix, P. Mendels, and F. Mila, eds.,Introduction to Frustrated Magnetism: Materials, Experiments, Theory, Vol. 164 (Springer, New York, 2011)

    2011

  2. [2]

    H. T. Diep, ed.,Frustrated Spin Systems(World Scien- tific, Singapore, 2013)

    2013

  3. [3]

    Balents, Spin liquids in frustrated magnets, Nature 464, 199 (2010)

    L. Balents, Spin liquids in frustrated magnets, Nature 464, 199 (2010)

    2010

  4. [4]

    Moessner and A

    R. Moessner and A. P. Ramirez, Geometrical frustration, Phys. Today59, 24 (2006)

    2006

  5. [5]

    J. O. Haerter and B. S. Shastry, Kinetic antiferromag- netism in the triangular lattice, Phys. Rev. Lett.95, 087202 (2005)

    2005

  6. [6]

    D. C. Mattis,The Theory of Magnetism I: Statics and Dynamics(Springer, Berlin, 1981) p. 258

    1981

  7. [7]

    Keeling, Quantum Magnetism

    J. Keeling, Quantum Magnetism

  8. [8]

    Tasaki,Physics and Mathematics of Quantum Many- Body Systems(Springer, Cham, 2020)

    H. Tasaki,Physics and Mathematics of Quantum Many- Body Systems(Springer, Cham, 2020)

    2020

Show all 91 references
  1. [9]

    D. P. Arovas, E. Berg, S. A. Kivelson, and S. Raghu, The Hubbard model, Annu. Rev. Condens. Matter Phys.13, 239 (2022)

    2022

  2. [10]

    Nagaoka, Ferromagnetism in a narrow, almost half- filledsband, Phys

    Y. Nagaoka, Ferromagnetism in a narrow, almost half- filledsband, Phys. Rev.147, 392 (1966)

    1966

  3. [11]

    Kim, Exact hole-induced resonating-valence-bond ground state in certainU=∞Hubbard models, Phys

    K.-S. Kim, Exact hole-induced resonating-valence-bond ground state in certainU=∞Hubbard models, Phys. Rev. B107, L140401 (2023)

    2023

  4. [12]

    C. N. Sposetti, B. Bravo, A. E. Trumper, C. J. Gazza, and L. O. Manuel, Classical antiferromagnetism in kinet- ically frustrated electronic models, Phys. Rev. Lett.112, 187204 (2014)

    2014

  5. [13]

    Glittum, A

    C. Glittum, A. ˇStrkalj, D. Prabhakaran, P. A. Goddard, C. D. Batista, and C. Castelnovo, A resonant valence bond spin liquid in the dilute limit of doped frustrated Mott insulators, Nat. Phys.21, 1211 (2025)

    2025

  6. [14]

    Poilblanc, Enhanced pairing in doped quantum mag- nets with frustrated hole motion, Phys

    D. Poilblanc, Enhanced pairing in doped quantum mag- nets with frustrated hole motion, Phys. Rev. Lett.93, 197204 (2004)

    2004

  7. [15]

    J. P. Dehollain, U. Mukhopadhyay, V. P. Michal, Y. Wang, B. Wunsch, C. Reichl, W. Wegscheider, M. S. Rudner, E. Demler, and L. M. K. Vandersypen, Nagaoka ferromagnetism observed in a quantum dot plaquette, Nature579, 528 (2020)

    2020

  8. [16]

    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, Nature629, 317 (2024)

    2024

  9. [17]

    M. L. Prichard, B. M. Spar, I. Morera, E. Demler, Z. Z. Yan, and W. S. Bakr, Directly imaging spin polarons in a kinetically frustrated Hubbard system, Nature629, 323 (2024)

    2024

  10. [18]

    Hanisch, B

    T. Hanisch, B. Kleine, A. Ritzl, and E. M¨ uller- Hartmann, Ferromagnetism in the Hubbard model: in- stability of the Nagaoka state on the triangular, honey- comb and kagome lattices, Ann. Phys.507, 303 (1995)

    1995

  11. [19]

    F. T. Lisandrini, B. Bravo, A. E. Trumper, L. O. Manuel, and C. J. Gazza, Evolution of Nagaoka phase with kinetic energy frustrating hopping, Phys. Rev. B95, 195103 (2017)

    2017

  12. [20]

    Gross and W

    C. Gross and W. S. Bakr, Quantum gas microscopy for single atom and spin detection, Nat. Phys.17, 1316 (2021)

    2021

  13. [21]

    G. M. Nixon, F. N. ¨Unal, and U. Schneider, Individually 6 tunable tunnelling coefficients in optical lattices using local periodic driving, Quantum Sci. Technol.9, 045030 (2024)

    2024

  14. [22]

    and superconducting qubits [55, 56]. Our findings motivate further studies of kinetic mag- netism on graphs that can explore (i) deeper connec- tions to polaron physics [39, 57] and effective spin models [5, 12], (ii) the physics of multiple holes, which is even richer and sen...

    2024

  15. [23]

    Gonz´ alez-Cuadra, D

    D. Gonz´ alez-Cuadra, D. Bluvstein, M. Kalinowski, R. Kaubruegger, N. Maskara, P. Naldesi, T. V. Zache, A. M. Kaufman, M. D. Lukin, H. Pichler, B. Vermersch, J. Ye, and P. Zoller, Fermionic quantum processing with programmable neutral atom arrays, Proc. Natl. Acad. Sci.120, e2...

    2023

  16. [24]

    S. B. Bravyi and A. Y. Kitaev, Fermionic quantum com- putation, Ann. Phys.298, 210 (2002)

    2002

  17. [25]

    Verstraete and J

    F. Verstraete and J. I. Cirac, Mapping local Hamiltonians of fermions to local Hamiltonians of spins, J. Stat. Mech. 2005, P09012 (2005)

    2005

  18. [26]

    Steudtner and S

    M. Steudtner and S. Wehner, Quantum codes for quan- tum simulation of fermions on a square lattice of qubits, Phys. Rev. A99, 022308 (2019)

    2019

  19. [27]

    S. H. Strogatz, Exploring complex networks, Nature410, 268 (2001)

    2001

  20. [28]

    M. E. J. Newman,Networks: An Introduction(Oxford University Press, Oxford, UK, 2018)

    2018

  21. [29]

    Barrat, M

    A. Barrat, M. Barthelemy, and A. Vespignani,Dynamical Processes on Complex Networks(Cambridge University Press, Cambridge, UK, 2008)

    2008

  22. [30]

    S. N. Dorogovtsev, A. V. Goltsev, and J. F. F. Mendes, Critical phenomena in complex networks, Rev. Mod. Phys.80, 1275 (2008)

    2008

  23. [31]

    R. M. D’Souza, J. G´ omez-Garde˜ nes, J. Nagler, and A. Arenas, Explosive phenomena in complex networks, Adv. Phys.68, 123 (2019)

    2019

  24. [32]

    Nokkala, J

    J. Nokkala, J. Piilo, and G. Bianconi, Complex quantum networks: a topical review, J. Phys. A57, 233001 (2024)

    2024

  25. [33]

    Zheng, D

    X. Zheng, D. Zeng, and F.-Y. Wang, Social balance in signed networks, Inf. Syst. Front.17, 1077 (2014)

    2014

  26. [34]

    Preethi and S

    G. Preethi and S. Dutta, Frustrated quantum mag- netism on complex networks: What sets the total spin, arXiv:2403.09116

  27. [35]

    [82, 83]

    See Supplemental Material for comparisons with Heisen- berg antiferromagnetism and data for random graphs of varying system size, which includes Refs. [82, 83]

  28. [36]

    F. H. Essler, H. Frahm, F. G¨ ohmann, A. Kl¨ umper, and V. E. Korepin,The One-Dimensional Hubbard Model (Cambridge University Press, Cambridge, UK, 2005)

    2005

  29. [37]

    Tasaki, Extension of Nagaoka’s theorem on the large- UHubbard model, Phys

    H. Tasaki, Extension of Nagaoka’s theorem on the large- UHubbard model, Phys. Rev. B40, 9192 (1989)

    1989

  30. [38]

    Bobrow, K

    E. Bobrow, K. Stubis, and Y. Li, Exact results on itin- erant ferromagnetism and the 15-puzzle problem, Phys. Rev. B98, 180101 (2018)

    2018

  31. [39]

    B. J. Powell, Balance and frustration in strongly cor- related itinerant electron systems: An extension of Na- gaoka’s theorem, Phys. Rev. B96, 174435 (2017)

    2017

  32. [40]

    Morera, A

    I. Morera, A. Bohrdt, W. W. Ho, and E. Demler, At- traction from kinetic frustration in ladder systems, Phys. Rev. Res.6, 023196 (2024)

    2024

  33. [41]

    H. Zhai, H. R. Larsson, S. Lee, Z.-H. Cui, T. Zhu, C. Sun, L. Peng, R. Peng, K. Liao, J. T¨ olle, J. Yang, S. Li, and G. K.-L. Chan,Block2: A comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond, J. Chem. ...

    2023

  34. [42]

    Sriram Shastry and B

    B. Sriram Shastry and B. Sutherland, Exact ground state of a quantum mechanical antiferromagnet, Physica B+C 108, 1069 (1981)

    1981

  35. [43]

    P. W. Leung and Y. F. Cheng, Absence of hole pairing in a simplet-Jmodel on the Shastry-Sutherland lattice, Phys. Rev. B69, 180403 (2004)

    2004

  36. [44]

    Holme, F

    P. Holme, F. Liljeros, C. R. Edling, and B. J. Kim, Net- work bipartivity, Phys. Rev. E68, 056107 (2003)

    2003

  37. [45]

    Aref and M

    S. Aref and M. C. Wilson, Measuring partial balance in signed networks, J. Complex Netw.6, 566 (2018)

    2018

  38. [46]

    Aref and M

    S. Aref and M. C. Wilson, Balance and frustration in signed networks, J. Complex Netw.7, 163 (2019)

    2019

  39. [47]

    Bayati, A

    M. Bayati, A. Montanari, and A. Saberi, Generating ran- dom networks without short cycles, Oper. Res.66, 1227 (2018)

    2018

  40. [48]

    Verstra¨ ete, Extremal problems for cycles in graphs, in Recent Trends in Combinatorics(Springer International Publishing, 2016) p

    J. Verstra¨ ete, Extremal problems for cycles in graphs, in Recent Trends in Combinatorics(Springer International Publishing, 2016) p. 83

    2016

  41. [49]

    Esslinger, Fermi-Hubbard physics with atoms in an optical lattice, Annu

    T. Esslinger, Fermi-Hubbard physics with atoms in an optical lattice, Annu. Rev. Condens. Matter Phys.1, 129 (2010)

    2010

  42. [50]

    Gross and I

    C. Gross and I. Bloch, Quantum simulations with ultra- cold atoms in optical lattices, Science357, 995 (2017)

    2017

  43. [51]

    Tarruell and L

    L. Tarruell and L. Sanchez-Palencia, Quantum simula- tion of the Hubbard model with ultracold fermions in optical lattices, C. R. Phys.19, 365 (2018)

    2018

  44. [52]

    G. Ji, M. Xu, L. H. Kendrick, C. S. Chiu, J. C. Br¨ uggenj¨ urgen, D. Greif, A. Bohrdt, F. Grusdt, E. Dem- ler, M. Lebrat, and M. Greiner, Coupling a mobile hole to an antiferromagnetic spin background: Transient dy- namics of a magnetic polaron, Phys. Rev. X11, 021022 (2021)

    2021

  45. [53]

    Chalopin, P

    T. Chalopin, P. Bojovi´ c, D. Bourgund, S. Wang, T. Franz, I. Bloch, and T. Hilker, Optical superlattice for engineering Hubbard couplings in quantum simula- tion, Phys. Rev. Lett.134, 053402 (2025)

    2025

  46. [54]

    Lloyd, Universal quantum simulators, Science273, 1073 (1996)

    S. Lloyd, Universal quantum simulators, Science273, 1073 (1996)

    1996

  47. [55]

    Bassman Oftelie, M

    L. Bassman Oftelie, M. Urbanek, M. Metcalf, J. Carter, A. F. Kemper, and W. A. de Jong, Simulating quantum materials with digital quantum computers, Quantum Sci. Technol.6, 043002 (2021)

    2021

  48. [56]

    Barends, L

    R. Barends, L. Lamata, J. Kelly, L. Garc ´ ıa- ´Alvarez, A. G. Fowler, A. Megrant, E. Jeffrey, T. C. White, D. Sank, J. Y. Mutus, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, I.-C. Hoi, C. Neill, P. J. J. O’Malley, C. Quintana, P. Roushan, A. Vainsencher, J. Wenner,...

    2015

  49. [57]

    Lamata, A

    L. Lamata, A. Parra-Rodriguez, M. Sanz, and E. Solano, Digital-analog quantum simulations with superconduct- ing circuits, Adv. Phys. X3, 1457981 (2018)

    2018

  50. [58]

    Samajdar and R

    R. Samajdar and R. N. Bhatt, Polaronic mechanism of Nagaoka ferromagnetism in Hubbard models, Phys. Rev. B109, 235128 (2024)

    2024

  51. [59]

    Doucot and X

    B. Doucot and X. G. Wen, Instability of the Nagaoka state with more than one hole, Phys. Rev. B40, 2719 (1989)

    1989

  52. [60]

    B. S. Shastry, H. R. Krishnamurthy, and P. W. Anderson, Instability of the Nagaoka ferromagnetic state of theU= ∞Hubbard model, Phys. Rev. B41, 2375 (1990)

    1990

  53. [61]

    J. A. Riera and A. P. Young, Ferromagnetism in the one- band Hubbard model, Phys. Rev. B40, 5285 (1989)

    1989

  54. [62]

    Ivantsov, A

    I. Ivantsov, A. Ferraz, and E. Kochetov, Breakdown of the Nagaoka phase at finite doping, Phys. Rev. B95, 155115 (2017). 7

    2017

  55. [63]

    H. B. Xavier, E. Kochetov, and A. Ferraz, Onset of ferromagnetism for strongly correlated electrons in one- dimensional chains, Phys. Rev. B101, 045112 (2020)

    2020

  56. [64]

    Zhang, W

    S.-S. Zhang, W. Zhu, and C. D. Batista, Pairing from strong repulsion in triangular lattice Hubbard model, Phys. Rev. B97, 140507 (2018)

    2018

  57. [65]

    S. Yun, W. Dobrautz, H. Luo, V. Katukuri, N. Lieber- mann, and A. Alavi, Ferromagnetic domains in the large- UHubbard model with a few holes: A full configuration interaction quantum Monte Carlo study, Phys. Rev. B 107, 064405 (2023)

    2023

  58. [66]

    L. Liu, H. Yao, E. Berg, S. R. White, and S. A. Kivel- son, Phases of the infiniteUHubbard model on square lattices, Phys. Rev. Lett.108, 126406 (2012)

    2012

  59. [67]

    Z. Zhu, D. N. Sheng, and A. Vishwanath, Doped Mott insulators in the triangular-lattice Hubbard model, Phys. Rev. B105, 205110 (2022)

    2022

  60. [68]

    Sharma, Y

    P. Sharma, Y. Peng, D. N. Sheng, H. J. Changlani, and Y. Wang, Instability of Nagaoka state and quan- tum phase transition via kinetic frustration control, arXiv:2508.08410

    arXiv

  61. [69]

    B´ eran, D

    P. B´ eran, D. Poilblanc, and R. Laughlin, Evidence for composite nature of quasiparticles in the 2Dt-Jmodel, Nucl. Phys. B473, 707 (1996)

    1996

  62. [70]

    C. S. Chiu, G. Ji, A. Bohrdt, M. Xu, M. Knap, E. Dem- ler, F. Grusdt, M. Greiner, and D. Greif, String patterns in the doped Hubbard model, Science365, 251 (2019)

    2019

  63. [71]

    Grusdt, A

    F. Grusdt, A. Bohrdt, and E. Demler, Microscopic spinon-chargon theory of magnetic polarons in thet-J model, Phys. Rev. B99, 224422 (2019)

    2019

  64. [72]

    Schl¨ omer, U

    H. Schl¨ omer, U. Schollw¨ ock, A. Bohrdt, and F. Grusdt, Kinetic-to-magnetic frustration crossover and linear con- finement in the doped triangulart-Jmodel, Phys. Rev. B110, L041117 (2024)

    2024

  65. [73]

    Watanabe and S

    Y. Watanabe and S. Miyashita, Existence of saturated ferromagnetic and spiral states in 1D Lieb-Ferrimagnetic models away from half-filling, J. Phys. Soc. Jpn.68, 3086 (1999)

    1999

  66. [74]

    Y. Li, K. Liu, and G. W. Bryant, Nagaoka ferromag- netism in 3×3 arrays and beyond, Phys. Rev. B110, 245141 (2024)

    2024

  67. [75]

    Mielke, Ferromagnetism in the Hubbard model on line graphs and further considerations, J

    A. Mielke, Ferromagnetism in the Hubbard model on line graphs and further considerations, J. Phys. A24, 3311 (1991)

    1991

  68. [76]

    Horiike and Y

    Y. Horiike and Y. Kawaguchi, A comprehensive ex- ploration of interaction networks reveals a connec- tion between entanglement and network structure, arXiv:2505.11466

    arXiv

  69. [77]

    Morera, M

    I. Morera, M. Kan´ asz-Nagy, T. Smolenski, L. Ciorciaro, A. Imamo˘ glu, and E. Demler, High-temperature kinetic magnetism in triangular lattices, Phys. Rev. Res.5, L022048 (2023)

    2023

  70. [78]

    R. C. Newby and E. Khatami, Finite-temperature kinetic ferromagnetism in the square-lattice Hubbard model, Phys. Rev. B111, 245120 (2025)

    2025

  71. [79]

    Pereira and E

    D. Pereira and E. J. Mueller, Kinetic magnetism in the crossover between the square and triangular lat- tice Fermi-Hubbard models, Phys. Rev. B112, 245120 (2025)

    2025

  72. [80]

    P. A. Lee, N. Nagaosa, and X.-G. Wen, Doping a Mott insulator: Physics of high-temperature superconductiv- ity, Rev. Mod. Phys.78, 17 (2006)

    2006

  73. [81]

    Shaping magnetic order by local frustration for itinerant fermions on a graph

    R. B. S and S. Dutta, Dataset for “Shaping magnetic order by local frustration for itinerant fermions on a graph”, Zenodo, 10.5281/zenodo.19019802 (2026)

    2026 doi

  74. [82]

    Shaping mag- netic order by local frustration for itinerant fermions on a graph

    R. B. S and S. Dutta, Source codes for “Shaping mag- netic order by local frustration for itinerant fermions on a graph”, Zenodo, 10.5281/zenodo.19028546 (2026)

    2026 doi

  75. [83]

    Kawamura, K

    M. Kawamura, K. Yoshimi, T. Misawa, Y. Yamaji, S. Todo, and N. Kawashima, Quantum lattice model solverHΦ, Comput. Phys. Commun.217, 180 (2017)

    2017

  76. [84]

    K. Ido, M. Kawamura, Y. Motoyama, K. Yoshimi, Y. Ya- maji, S. Todo, N. Kawashima, and T. Misawa, Update ofHΦ: Newly added functions and methods in versions 2 and 3, Comput. Phys. Commun.298, 109093 (2024)

    2024

  77. [85]

    Grimm, M

    R. Grimm, M. Weidem¨ uller, and Y. B. Ovchinnikov, Op- tical dipole traps for neutral atoms, Adv. At. Mol. Opt. Phys.42, 95 (2000)

    2000

  78. [86]

    Bloch and M

    I. Bloch and M. Greiner, Exploring quantum matter with ultracold atoms in optical lattices, Adv. At. Mol. Opt. Phys.52, 1 (2005)

    2005

  79. [87]

    Bloch, J

    I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys.80, 885 (2008)

    2008

  80. [88]

    C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Fesh- bach resonances in ultracold gases, Rev. Mod. Phys.82, 1225 (2010)

    2010

  81. [89]

    Weitenberg, M

    C. Weitenberg, M. Endres, J. F. Sherson, M. Cheneau, P. Schauß, T. Fukuhara, I. Bloch, and S. Kuhr, Single- spin addressing in an atomic Mott insulator, Nature471, 319 (2011)

    2011

  82. [90]

    Zupancic, P

    P. Zupancic, P. M. Preiss, R. Ma, A. Lukin, M. Eric Tai, M. Rispoli, R. Islam, and M. Greiner, Ultra-precise holo- graphic beam shaping for microscopic quantum control, Opt. Express24, 13881 (2016)

    2016

  83. [91]

    Shaping Magnetic Order by Local Frustration for Itinerant Fermions on a Graph

    M. Lebrat, A. Kale, L. H. Kendrick, M. Xu, Y. Gang, A. Nikolaenko, P. M. Bonetti, S. Sachdev, and M. Greiner, Ferrimagnetism of ultracold fermions in a multi-band Hubbard system, arXiv:2404.17555 End Matter Appendix A: Square grid with a frustrated plaque- tte—The ordering of ...

    2017 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.