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Antiferromagnetism and Tightly Bound Cooper Pairs Induced by Kinetic Frustration

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Pith's one-line read Kinetic frustration of hole motion—competing nearest- and next-nearest-neighbor hopping—can stabilize antiferromagnetism and d-wave Cooper pairing at the same time in the square-lattice t-J model.

desk verdict A genuinely new kinetic-frustration pairing mechanism against a dynamically stabilized AFM background, with a clean solvable limit and consistent ED/DMRG correlations, but the headline binding gap is not yet directly benchmarked. read the letter →

arxiv 2506.16464 v2 pith:RJHKEVYW submitted 2025-06-19 cond-mat.str-el cond-mat.supr-con

Yixin Zhang , Cristian Batista , Yang Zhang This is my paper · ORCID
classification cond-mat.str-elcond-mat.supr-con PACS 71.10.Fd74.20.Mn75.10.Jm
keywords kineticfrustrationantiferromagnetismd-wavesuperconductivityt-JmodelHubbardCooperpairsMottinsulatorantiferromagneticpolaron
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 claims that kinetic frustration of hole motion—competing nearest-neighbor ($t_1$) and next-nearest-neighbor ($t_2$) hopping—can make antiferromagnetism and superconductivity cooperate rather than compete in a doped Mott insulator. In an extended square-lattice $t$–$J$ model, a hole moving against a Néel background forms an antiferromagnetic polaron: local singlet bonds around the hole lower its kinetic energy. Two holes on opposite sublattices cooperatively strengthen the singlet character of the two bonds parallel to their separation, producing a $d_{x^2-y^2}$ Cooper pair with no bare attractive force. The calculation reports a two-hole binding gap of about $0.19t_1$ and a coherence length of roughly six lattice spacings at $U=10t_1$, $t_2=0.6t_1$, while the same mechanism makes a third hole repulsive and suppresses phase separation. If correct, this gives a minimal framework in which strong-coupling $d$-wave superconductivity coexists with long-range antiferromagnetic order.

What carries the argument

The central object is the antiferromagnetic polaron: a hole dressed by enhanced singlet correlations on surrounding bonds, which lowers kinetic energy by relieving destructive interference between $t_1$ and $t_2$ hopping paths. This is the counter-Nagaoka effect, in which kinetic frustration favors antiparallel spins instead of the ferromagnetism of Nagaoka's theorem. The paper tracks the conditional spin-spin correlation $M_{i,j;(k,l,\ldots)}$, which rises to about $0.82$ on the bonds parallel to an adjacent hole pair, and rewrites the kinetic energy in terms of an effective two-body hopping amplitude $\tilde{t}_{jk}(l)$ that is largest when the fixed hole $l$ is adjacent to bond $jk$. A two-particle model built from these amplitudes reproduces the coherence length of the full constrained calculation, showing that the polaronic two-body hopping, not the Ising attraction, is the dominant pairing mechanism.

What would settle it

Decisive check: compute the two-hole binding gap with large-bond-dimension density-matrix renormalization group on the $8\times 16$ cylinder at $\lambda=\Delta=1$, $U=10t_1$, $t_2=0.6t_1$; if the gap is not near $0.19t_1$ or the pair correlation length is not near six lattice spacings, the polaronic two-body hopping is not the dominant pairing glue.

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Extended reading notes

Core claim

The paper's central claim is that the very same kinetic frustration that stabilizes Néel order in the doped square-lattice Hubbard model also supplies the pairing glue. A hole moving by $t_2$ hopping against an antiferromagnetic background gains kinetic energy by forming a local singlet on the bonds that complete a triangle with the hole; the singlet acts like a $\pi$-flux and relieves destructive interference between competing hopping paths. When a second hole sits on the opposite sublattice next to the first, the two holes cooperatively enhance singlet correlations on the two bonds parallel to their separation, from about $0.58$ far from the holes to roughly $0.82$ on those bonds, and this correlated two-body hopping binds the pair without any attractive interaction. The authors establish the mechanism by solving an exactly solvable limit ($\lambda=\Delta=0$), then show that turning on kinetic and spin fluctuations along an adiabatic path raises the binding gap to approximately $0.19t_1$ and shrinks the coherence length to about six lattice spacings at $U=10t_1$, $t_2=0.6t_1$, with $d_{x^2-y^2}$ pairing symmetry throughout.

Load-bearing premise

The calculation assumes that spin fluctuations far from a hole add the same energy regardless of where the other hole sits, so they can be omitted from the quantum-state space; if that near-sightedness fails, the small binding gap and short coherence length could be artifacts of the truncation.

Editorial extensions

If this is right

  • At $U=10t_1$, $t_2=0.6t_1$, the two-hole binding gap reaches about $0.19t_1$ and the Cooper-pair coherence length is near six lattice spacings, so the pairs are tightly bound in real space.
  • The pairing symmetry is $d_{x^2-y^2}$ in both the exactly solvable limit and the full isotropic model, with the binding gap staying open along the $(\lambda,\Delta)$ path, so the same mechanism governs both extremes.
  • The singlet-formation glue suppresses phase separation: a third hole repels a preformed pair, and the four-hole ground state consists of two well-separated Cooper pairs.
  • At higher doping, overlapping antiferromagnetic polarons should turn the Néel state into a quantum paramagnet with a spin gap inside the superconducting phase.
  • In the dilute preformed-pair regime the binding-gap results imply a transition temperature of about $k_B T_c \approx 1.16\,\rho_h t_1$.

Reading between the lines

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

  • Extension the authors leave implicit: the local signature—conditional singlet correlations near $0.82$ on bonds parallel to a pinned hole pair—could be measured directly with a quantum gas microscope on ultracold fermions in an optical lattice, offering a clean test of the polaronic glue.
  • The adiabatic-continuity argument suggests the same $d$-wave pairing should appear for parameter regions preserving the sign of $t_1^2t_2$; tuning $t_2/t_1$ in unbiased numerics should show the coherence length growing exponentially as $t_2/t_1\to 0$, exactly as the solvable limit predicts.
  • The authors do not identify the high-doping quantum paramagnet; computing the spin gap and any topological invariants in the four- or eight-hole-doped regime would test whether this 'bipolaron liquid' connects to a resonating-valence-bond state.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper studies the square-lattice generalized t-J model with nearest-neighbor hopping λt1, next-nearest-neighbor hopping t2, exchange couplings J1,J2, and correlated hopping, derived as the large-U limit of an extended Hubbard model. The authors claim that kinetic frustration arising from competing t1 and t2 stabilizes Néel antiferromagnetic order and, upon doping, induces tightly bound d-wave Cooper pairs, with a binding gap Δg≈0.19t1 and coherence length ξ≈6.3 at U=10t1, λ=Δ=1. The argument uses an exactly solvable t2-only/Ising limit (λ=Δ=0), a constrained ED method on 8×8 and 16×16 clusters, and DMRG on 8×16 cylinders; the two numerical methods are compared through hole-hole and spin correlations. The paper further constructs an effective two-body hopping model to identify singlet-enhanced hopping as the pairing glue and argues that the same mechanism suppresses phase separation.

Significance. Should the quantitative claims survive, this is a significant contribution: it offers a minimal microscopic route to coexisting AFM order and d-wave superconductivity, with an exactly solvable limit that fixes the pairing symmetry and an explicit local pairing 'glue' based on enhanced singlet bonds around hole pairs. Strengths include the rigorous λ=Δ=0 solution and d-wave derivation, the quantitative ED-DMRG agreement on hole-hole and spin correlations at the isotropic point, and an insightful effective two-body hopping decomposition that reproduces a short coherence length. The main weakness is that the headline binding gap, which underlies the tight-binding and adiabatic-continuity claims, is computed in a variational truncated space whose energy errors are not benchmarked against an independent method.

major comments (3)
  1. [Sec. III; Fig. 4; SM Appendix C] The central binding-gap metric Δg=E1−E0 is computed only in the constrained Hilbert space and is not validated against an independent energy gap. The DMRG benchmark (Fig. 3, Fig. S5) compares the hole density correlation Pij at (λ,Δ)=(1,1), not the energies; Table I gives DMRG ground-state energies but no DMRG binding gap. Because the basis enlargement scheme (SM C) deliberately increases Df for close hole pairs to restore Nfl/Nkin, it grants close pairs more variational freedom than separated pairs, which can lower E0 relative to E1 and inflate Δg. I request a direct DMRG estimate of the two-hole gap in a matched momentum sector, or a basis-convergence study of E0 and E1 on clusters where exact ED is feasible. Without this, the value Δg≈0.19t1 is not quantitatively established.
  2. [Sec. III; SM Appendix C] The adiabatic-continuity claim is only demonstrated inside the truncated space, whose reliability the authors themselves state is parameter-dependent. The text says the basis is optimized for regimes where both λ and Δ are nonzero, and SM Appendix C reports that at (λ,Δ)=(0,1) the truncation can artificially enhance pairing (Fig. S6(c)). Since the path (0,0)→(1,0)→(1,1) is used to argue that the gap never closes and connects to the exactly solvable limit, convergence checks at multiple intermediate points, including (1,0) and points with small λ at Δ=1, are needed before the full-Hilbert-space gap can be claimed to remain open along the entire path.
  3. [Sec. IV; SM Appendix E] The effective two-body hopping model is presented as corroboration of the tight-binding scale, but it is a derived diagnostic rather than an independent validation. The amplitudes t~jk(l) in Fig. 6 are extracted from the same DMRG/ED ground states, their values beyond the cluster are assumed, and the resulting coherence length depends on whether the Ising attraction J1/2 is added (ξ=9.6 without, 4.6 with, versus 6.3 from ED). The agreement is encouraging but does not independently constrain Δg; please state this limitation explicitly and report the uncertainty associated with the long-distance extrapolation.
minor comments (5)
  1. [Abstract; Sec. VI] Terms such as 'superconducting phase' and 'coherent d-wave superconducting channel' overstate what is shown by two-hole binding and correlation data; I suggest qualifying them as pairing correlations and a pairing channel.
  2. [Sec. III] Page 5 contains a typo: 'the extended tJ model is not longer valid' should read 'is no longer valid'.
  3. [Fig. 4] The caption should specify that the color scale is Δg/t1 and define the plotted quantity; the current text says 'Energy Gap Δg/t1' but the figure's colorbar is not labeled with units.
  4. [Eq. (5)] The notation Mi,j,(k,l,m···) is hard to parse; I recommend defining the fixed-hole set once and writing Mi,j({k,l,...}) consistently.
  5. [Acknowledgments] The name 'Philip Philips' should be 'Philip Phillips'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the binding gap, d-wave symmetry, and coherence length are computed directly from the model and cross-checked with DMRG; admitted truncation limitations are correctness risks, not circular inputs.

full rationale

The paper's derivation chain is self-contained. The exactly solvable (λ,Δ)=(0,0) limit is solved in the paper itself (SM Appendices A-B): the two-hole wavefunction and its d-wave sign structure follow from minimizing the t2-kinetic-energy bound, not from an assumed pairing ansatz. The d-wave symmetry is independently confirmed by DMRG pair-pair correlators (SM Fig. S8). The binding gap Δg(k)=E1(k)-E0(k) at k=(0,2π/L) is a direct spectral energy difference in constrained ED; no parameter was fitted to the gap and no DMRG binding gap was used as input. The truncated Hilbert-space scheme is benchmarked against DMRG through the hole-hole correlator Pi,j at (λ,Δ)=(1,1) (SM Fig. S5) and then used to compute gaps along the path; this is a validation of a variational basis, not a fit of the predicted quantity. The effective two-body hopping amplitudes t̃jk(l) are an exact reformulation of the kinetic energy (Eqs. 6-8), and the effective-model coherence length is presented as a consistency check, not as an independent first-principles prediction. The paper explicitly flags its own limitation that the basis is unreliable at (λ,Δ)=(0,1) and avoids that point on the adiabatic path; this is a correctness caveat, not circularity. Self-citations (refs. 23-25, 30, 44-45) appear in background and motivation, but the load-bearing arguments—the kinetic-energy bound, the exact two-hole solution, the constrained-ED gap, and the DMRG d-wave correlations—do not reduce to those citations. No step satisfies the standard of Eq. X = Eq. Y by construction or a fitted parameter renamed as a prediction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

No new particles or forces are introduced. The AFM polaron is a composite quasiparticle (hole plus local singlet distortion) rather than a new fundamental entity, and the "opposite effective charges" in the abstract are a rhetorical analogy for sublattice-dependent attraction, not a new conserved charge. The model parameters t2/t1 and U/t1 are inputs, and the truncation parameters are numerical controls. The core load rests on the near-sightedness assumption for the constrained ED and on the numerical benchmark against DMRG.

free parameters (3)
  • t2/t1 ratio = 0.6
    Chosen by hand inside the intermediate regime (0.5, 0.7) where kinetic frustration and J1 exchange cooperatively stabilize Néel order; the paper says "For all subsequent calculations, we adopt t2 = 0.6t1" (Sec. III). The central pairing results depend on this ratio.
  • U/t1 interaction strength = 10 (also 1 to 5 used for the adiabaticity sweep)
    Picked as a realistic strong-coupling value for the t-J derivation; the paper also runs the extended t-J model at unrealistically small U/t1 to demonstrate adiabatic continuity, explicitly noting the model is invalid there (Sec. IV, Fig. 4 caption).
  • Truncation scheme parameters (D_k, D_f, and hierarchical enlargement priorities) = D_k=1, D_f=2, plus a hierarchy that stops when max_i,j N_fl(rho)/N_kin(rho) is fixed
    The Hilbert space truncation is calibrated to reproduce DMRG hole-hole correlations at (λ,Δ)=(1,1); Appendix C and Fig. S5 show alternative schemes give poorer agreement, so the chosen scheme is tuned to the benchmark.
assumptions (5)
  • domain assumption The fourth-order canonical perturbation expansion of the Hubbard model gives the effective t-J-H_c_h Hamiltonian (Eqs. 1-3) with J1=4t1^2/U, J2=4t2^2/U.
    Standard strong-coupling derivation, cited to Chao et al. [33] and Zhang-Rice [35]; all subsequent physics uses this effective Hamiltonian.
  • domain assumption Near-sightedness of spin fluctuations: configurations with spin flips beyond threshold distance D_f from each hole contribute almost identically for any hole separation and cancel in binding-energy differences.
    This is the central premise of the constrained ED method (Appendix C: "spin fluctuations far from the holes contribute nearly identically regardless of the hole separation, and therefore cancel out in binding energy calculations").
  • domain assumption Adiabatic continuity: the two-hole binding gap does not close along the (λ,Δ) path from (0,0) to (1,1), so the pairing mechanism and d-wave symmetry in the solvable limit carry over to the full isotropic model.
    Verified only numerically within truncated Hilbert spaces (Sec. III, Fig. 4), and the path includes U/t1 values where the model is invalid; not a rigorous proof.
  • domain assumption The first excited state at momentum k=(0,2π/L) in the two-hole system represents the scattering continuum in the thermodynamic limit, making E1(k)-E0(k) a binding gap.
    Argued in Sec. III and SM Appendix C.4 by comparing correlation patterns in different sectors (Fig. S7); a numerical identification, not a theorem.
  • domain assumption The effective two-body hopping amplitudes t̃jk(l) extracted at the largest separation in the finite cluster remain unchanged at larger distances in the thermodynamic limit.
    Explicitly stated in Sec. IV: "We assumed that these amplitudes remain unchanged beyond the largest distances accessible in the cluster." This is used to compute ξ=9.6 and ξ=4.6.

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Pith. "Pith review of Antiferromagnetism and Tightly Bound Cooper Pairs Induced by Kinetic Frustration." pith.science (2026). https://pith.science/paper/RJHKEVYW

@misc{pith2026250616464,
  author       = {Pith},
  title        = {Pith review of: Antiferromagnetism and Tightly Bound Cooper Pairs Induced by Kinetic Frustration},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RJHKEVYW}},
  note         = {Machine review of arXiv:2506.16464}
}
abstract

Antiferromagnetism and superconductivity are often viewed as competing orders in correlated electron systems. Here, we demonstrate that kinetic frustration in hole motion facilitates their coexistence within the square-lattice repulsive Hubbard model. Combining exact analytical solutions on tailored geometries with large-scale numerical simulations, we reveal a robust pairing mechanism: holes on opposite sublattices behave as if they carry opposite effective charges due to spin singlet formation from kinetic frustration. This emergent property suppresses phase separation and fosters a coherent $d$-wave superconducting channel embedded within a long-range antiferromagnetic background. Our findings establish a minimal yet broadly applicable framework for stabilizing strong-coupling superconductivity in doped Mott insulators.

Figures

Figures reproduced from arXiv: 2506.16464 by the authors.

Figure 1
Figure 1. FIG. 1. Antiferromagnetic polaron induced by kinetic frus [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Hole-hole correlation [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. FIG. 5. (a) Spin-spin correlations [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figures from the paper (2 more)
Figure 6
Figure 6. Figure 6: (a, b) shows the effective two-body hopping am￾plitudes t˜jk(l) computed with DMRG for two holes on an 8-leg cylinder of length Lx = 16. As anticipated from [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Schematic diagram illustrating the suppression of [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

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

  1. Exact Nagaoka-to-spiral transition in the doped infinite-U triangular lattice

    cond-mat.str-el 2026-07 conditional novelty 7.0 of 10

    A single hole in the infinite-U triangular Hubbard model destabilizes Nagaoka ferromagnetism at t2,c/t1 = -0.182, giving way to a long-wavelength spin spiral.

Reference graph

Works this paper leans on

77 extracted references · 62 canonical work pages · cited by 1 Pith paper

  1. [1]

    P. A. Lee, N. Nagaosa, and X.-G. Wen, Doping a mott in- sulator: Physics of high-temperature superconductivity, Rev. Mod. Phys.78, 17 (2006)

    2006

  2. [2]

    J. D. Thompson, M. Nicklas, A. Bianchi, R. Movshovich, A. Llobet, W. Bao, A. Malinowski, M. F. Hundley, N. O. Moreno, P. G. Pagliuso, J. L. Sarrao, S. Nakatsuji, Z. Fisk, R. Borth, E. Lengyel, N. Oeschler, G. Sparn, and F. Steglich, Magnetism and unconventional superconduc- tivity in cenmmin3n+2m heavy-fermion crystals, Physica B: Condensed Matter329–333,...

    work page 2003

  3. [3]

    Kanoda and R

    K. Kanoda and R. Kato, Mott physics in organic con- ductors with triangular lattices, Annual Review of Con- densed Matter Physics2, 167 (2011)

    2011

  4. [4]

    G. R. Stewart, Superconductivity in iron compounds, Rev. Mod. Phys.83, 1589 (2011)

    2011

  5. [5]

    Keimer, S

    B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, and J. Zaanen, From quantum matter to high-temperature superconductivity in copper oxides, Nature 518, 179 (2015)

    2015

  6. [6]

    Dagotto, Correlated electrons in high-temperature su- perconductors, Rev

    E. Dagotto, Correlated electrons in high-temperature su- perconductors, Rev. Mod. Phys.66, 763 (1994)

    1994

  7. [7]

    N. E. Bickers, D. J. Scalapino, and S. R. White, Con- serving approximations for strongly fluctuating electron systems. i. formalism and calculational approach, Phys. Rev. Lett.62, 961 (1989)

    work page 1989

  8. [8]

    Monthoux and D

    P. Monthoux and D. J. Scalapino, Self-consistentdx2−y2 pairing in a two-dimensional hubbard model, Phys. Rev. Lett. 67, 3448 (1991)

    work page 1991

Show all 77 references
  1. [9]

    D. J. Scalapino, Numerical studies of the 2d hubbard model, Handbook of High-Temperature Superconductiv- ity: Theory and Experiment , 495 (2007), also available as arXiv:cond-mat/0610710

    2007 arXiv

  2. [10]

    V. J. Emery, S. A. Kivelson, and H. Q. Lin, Phase sepa- ration in the t-j model, Phys. Rev. Lett.64, 475 (1990)

    1990

  3. [11]

    Moreo and E

    A. Moreo and E. Dagotto, Phase separation scenario for high-temperature superconductors, Phys. Rev. B43, 11442 (1991)

    1991

  4. [12]

    M. A. Kastner, R. J. Birgeneau, G. Shirane, and Y. En- doh, Magnetic, transport, and optical properties of monolayer copper oxides, Rev. Mod. Phys. 70, 897 (1998)

    1998

  5. [13]

    Armitage, P

    N. Armitage, P. Fournier, and R. Greene, Progress and perspectives on electron-doped cuprates, Reviews of Modern Physics82, 2421 (2010)

    2010

  6. [14]

    C.Stock, C.Broholm, J.Hudis, H.J.Kang,andC.Petro- vic,Spinresonanceinthed-wavesuperconductorcecoin 5, Physical Review Letters100, 087001 (2008)

    2008

  7. [15]

    Lefebvre, P

    S. Lefebvre, P. Wzietek, S. Brown, C. Bourbonnais, D. Jérome, C. Mézière, M. Fourmigué, and P. Batail, Mott transition, antiferromagnetism, and unconventional superconductivity in layered organic superconductors, Physical Review Letters85, 5420 (2000)

    2000

  8. [16]

    Timm and K

    C. Timm and K. Bennemann, Doping dependence of the néel temperature in mott-hubbard antiferromagnets: ef- fect of vortices, Physical Review Letters84, 4994 (2000)

    2000

  9. [17]

    E. Berg, E. Fradkin, S. A. Kivelson, and J. M. Tran- quada, Striped superconductors: how spin, charge and superconducting orders intertwine in the cuprates, New Journal of Physics11, 115004 (2009)

    2009

  10. [18]

    Zheng, C.-M

    B.-X. Zheng, C.-M. Chung, P. Corboz, G. Ehlers, M.-P. Qin, R. M. Noack, H. Shi, S. R. White, S. Zhang, and G. K.-L. Chan, Stripe order in the underdoped region of the two-dimensional hubbard model, Science358, 1155 (2017)

    2017

  11. [19]

    E. W. Huang, C. B. Mendl, S. Liu, S. Johnston, H.-C. Jiang, B. Moritz, and T. P. Devereaux, Numerical evi- dence of fluctuating stripes in the normal state of high-t c cuprate superconductors, Science358, 1161 (2017)

    2017

  12. [20]

    S. Gong, W. Zhu, and D. Sheng, Robust d-wave super- conductivity in the square-lattice t-j model, Physical Re- view Letters127, 097003 (2021)

    2021

  13. [21]

    Zhang, Coexistence of superconductivity with par- tially filled stripes in the hubbard model, Science384, eadh7691 (2024)

    H.Xu, C.-M.Chung, M.Qin, U.Schollwöck, S.R.White, and S. Zhang, Coexistence of superconductivity with par- tially filled stripes in the hubbard model, Science384, eadh7691 (2024)

    2024

  14. [22]

    F. Chen, F. Haldane, and D. Sheng, Global phase dia- gram of d-wave superconductivity in the square-lattice tj model, Proceedings of the National Academy of Sciences 122, e2420963122 (2025)

    2025

  15. [23]

    Isaev, G

    L. Isaev, G. Ortiz, and C. Batista, Superconductivity in strongly repulsive fermions: The role of kinetic-energy frustration, Physical review letters105, 187002 (2010)

    2010

  16. [24]

    Zhang, W

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

    2018

  17. [25]

    K. G. Nazaryan and L. Fu, Magnonic superconductivity, Science Advances10, 10.1126/sciadv.adp5681 (2024)

    2024 doi

  18. [26]

    J. O. Haerter and B. S. Shastry, Kinetic antiferromag- netism in the triangular lattice, Physical review letters 95, 087202 (2005)

    2005

  19. [27]

    C. N. Sposetti, B. Bravo, A. E. Trumper, C. J. Gazza, and L. O. Manuel, Classical Antiferromagnetism in Ki- netically Frustrated Electronic Models, Physical Review Letters 112, 187204 (2014)

    2014

  20. [28]

    Ciorciaro, T

    L. Ciorciaro, T. Smoleński, I. Morera, N. Kiper, S. Hies- tand, M. Kroner, Y. Zhang, K. Watanabe, T. Taniguchi, E. Demler, and A. İmamoğlu, Kinetic magnetism in tri- angular moirématerials, Nature623, 509 (2023)

    2023

  21. [29]

    Kim, Exact hole-induced resonating-valence-bond ground state in certain U=∞ Hubbard models, Physical Review B107, L140401 (2023)

    K.-S. Kim, Exact hole-induced resonating-valence-bond ground state in certain U=∞ Hubbard models, Physical Review B107, L140401 (2023)

    2023

  22. [30]

    Zhang and L

    Y. Zhang and L. Fu, Pseudogap metal and magnetization plateau from doping moiré mott insulator, SciPost Phys. Core 6, 038 (2023). 10

    2023

  23. [31]

    Leiner, V

    J. Leiner, V. Thampy, A. D. Christianson, D. L. Aber- nathy, M. B. Stone, M. D. Lumsden, A. S. Sefat, B. C. Sales, J. Hu, Z. Mao, W. Bao, and C. Broholm, Modified magnetism within the coherence volume of superconduct- ing fe1+δsexte1−x, Physical Review B90, 100501 (2014)

    2014

  24. [32]

    M. Xu, L. H. Kendrick, A. Kale, Y. Gang, C. Feng, S. Zhang, A. W. Young, M. Lebrat, and M. Greiner, A neutral-atom hubbard quantum simulator in the cryo- genic regime, arXiv preprint arXiv:2502.00095 (2025)

    2025 arXiv

  25. [33]

    K. Chao, J. Spałek, and A. Oleś, Canonical perturbation expansion of the hubbard model, Physical Review B18, 3453 (1978)

    1978

  26. [34]

    S. A. Trugman, Interaction of holes in a Hubbard an- tiferromagnet and high-temperature superconductivity, Physical Review B 37, 1597 (1988), publisher: Ameri- can Physical Society

    1988

  27. [35]

    Zhang and T

    F. Zhang and T. Rice, Effective hamiltonian for the su- perconducting cu oxides, Physical Review B 37, 3759 (1988)

    1988

  28. [36]

    Nagaoka, Ferromagnetism in a Narrow, Almost Half- Filled $s$ Band, Physical Review147, 392 (1966), pub- lisher: American Physical Society

    Y. Nagaoka, Ferromagnetism in a Narrow, Almost Half- Filled $s$ Band, Physical Review147, 392 (1966), pub- lisher: American Physical Society

    1966

  29. [37]

    Tasaki, Extension of Nagaoka’s theorem on the large- U Hubbard model, Physical Review B40, 9192 (1989), publisher: American Physical Society

    H. Tasaki, Extension of Nagaoka’s theorem on the large- U Hubbard model, Physical Review B40, 9192 (1989), publisher: American Physical Society

    1989

  30. [38]

    H. Tasaki, From Nagaoka’s ferromagnetism to flat-band ferromagnetism and beyond: An introduction to ferro- magnetism in the Hubbard model, Progress of Theoreti- cal Physics99, 489 (1998), arXiv:cond-mat/9712219

    1998 arXiv

  31. [39]

    A. A. Gangat, Weak first-order phase transitions in the frustrated square lattice j 1- j 2 classical ising model, Physical Review B109, 104419 (2024)

    2024

  32. [40]

    Morita, R

    S. Morita, R. Kaneko, and M. Imada, Quantum Spin Liquid in Spin 1/2 J1–J2 Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections, Journal of the Physical Society of Japan84, 024720 (2015), pub- lisher: The Physi...

    2015

  33. [41]

    S. R. White, Density matrix formulation for quantum renormalizationgroups,Phys.Rev.Lett. 69,2863(1992)

    1992

  34. [42]

    J. R. Schrieffer, X.-G. Wen, and S.-C. Zhang, Spin-bag mechanism of high-temperature superconductivity, Phys- ical Review Letters60, 944 (1988), publisher: American Physical Society

    1988

  35. [43]

    Z. Y. Weng, Mobile spin bags and their interaction in the spin-density-wave background, Physical Review B 41, 1990 (1990)

    1990

  36. [44]

    Davydova, Y

    M. Davydova, Y. Zhang, and L. Fu, Itinerant spin polaron and metallic ferromagnetism in semiconductor moir\’e superlattices, Physical Review B 107, 224420 (2023), publisher: American Physical Society

    2023

  37. [45]

    B. A. Foutty, J. Yu, T. Devakul, C. R. Kometter, Y. Zhang, K. Watanabe, T. Taniguchi, L. Fu, and B. E. Feldman, Tunable spin and valley excitations of corre- lated insulators inγ-valley moiré bands, Nature Materi- als 22, 731 (2023)

    2023

  38. [46]

    Z. Tao, W. Zhao, B. Shen, T. Li, P. Knüppel, K. Watan- abe, T. Taniguchi, J. Shan, and K. F. Mak, Observation of spin polarons in a frustrated moiré hubbard system, Nature Physics20, 783 (2024)

    2024

  39. [47]

    Jiang and T

    H.-C. Jiang and T. P. Devereaux, Superconductivity in the doped hubbard model and its interplay with next- nearest hoppingt′, Science365, 1424 (2019)

    2019

  40. [48]

    Prokof’ev, O

    N. Prokof’ev, O. Ruebenacker, and B. Svistunov, Critical point of a weakly interacting two-dimensional bose gas, Physical Review Letters87, 270402 (2001)

    2001

  41. [49]

    H.-C.JiangandS.A.Kivelson,HighTemperatureSuper- conductivity in a Lightly Doped Quantum Spin Liquid, Physical Review Letters127, 097002 (2021), publisher: American Physical Society

    2021

  42. [50]

    Jiang, S

    H.-C. Jiang, S. A. Kivelson, and D.-H. Lee, Supercon- ducting valence bond fluid in lightly doped eight-leg t-j cylinders, Physical Review B108, 054505 (2023)

    2023

  43. [51]

    S. A. Trugman, Spectral function of a hole in a Hubbard antiferromagnet, Physical Review B41, 892 (1990), pub- lisher: American Physical Society

    1990

  44. [52]

    J. R. Schrieffer, X. G. Wen, and S. C. Zhang, Dynamic spin fluctuations and the bag mechanism of high-Tc su- perconductivity, Phys. Rev. B39, 11663 (1989)

    1989

  45. [53]

    Baskaran, Z

    G. Baskaran, Z. Zou, and P. W. Anderson, The resonat- ing valence bond state and high-Tc superconductivity — A mean field theory, Solid State Communications63, 973 (1987)

    1987

  46. [54]

    P. W. Anderson, The Resonating Valence Bond State in La2CuO4 and Superconductivity, Science235, 1196 (1987), publisher: American Association for the Ad- vancement of Science

    1987

  47. [55]

    P. W. Anderson, P. A. Lee, M. Randeria, T. M. Rice, N. Trivedi, and F. C. Zhang, The physics behind high- temperature superconducting cuprates: the plain vanilla version of rvb, Journal of Physics: Condensed Matter16, R755 (2004)

    2004

  48. [56]

    Wietek, L

    A. Wietek, L. Staszewski, M. Ulaga, P. L. Ebert, H. Karlsson, S. Sarkar, H. Shackleton, A. Sinha, and R. D. Soares, Xdiag: Exact diagonalization for quan- tum many-body systems (2025), arXiv:2505.02901 [cond- mat.str-el]

    2025 arXiv

  49. [57]

    Weinberg and M

    P. Weinberg and M. Bukov, Quspin: a python package for dynamics and exact diagonalisation of quantum many body systems part i: spin chains, SciPost Phys.2, 003 (2017)

    2017

  50. [58]

    Weinberg and M

    P. Weinberg and M. Bukov, QuSpin: a Python package for dynamics and exact diagonalisation of quantum many body systems. Part II: bosons, fermions and higher spins, SciPost Physics7, 020 (2019)

    2019

  51. [59]

    de Llano, A

    M. de Llano, A. Salazar, and M. A. Solis, Two- dimensional delta potential wells and condensed-matter physics (2003), rev. Mex. Fís. 51, 626–632 (2005), arXiv:cond-mat/0305631 [cond-mat.supr-con]

    2003 arXiv

  52. [60]

    Nath and N

    S. Nath and N. K. Ghosh, Phonon-mediated elec- tron–phonon interaction in hubbard–holstein model, J. Low Temp. Phys.182, 1 (2016)

    2016

  53. [61]

    J.-Y. Zhao, S. A. Chen, H.-K. Zhang, and Z.-Y. Weng, Two-Hole Ground State: Dichotomy in Pairing Symme- try, Physical Review X 12, 011062 (2022), publisher: American Physical Society

    2022

  54. [62]

    Fishman, S

    M. Fishman, S. White, and E. M. Stoudenmire, The iten- sor software library for tensor network calculations, Sci- Post Physics Codebases , 004 (2022)

    2022

  55. [63]

    M.Fishman, S.White,andE.M.Stoudenmire,Codebase release 0.3 for itensor, SciPost Physics Codebases , 004 (2022). 11 SUPPLEMENTARY MATERIAL FOR: ANTIFERROMAGNETISM AND TIGHTLY BOUND COOPER PAIRS INDUCED BY KINETIC FRUSTRATION Appendix A: The Kinetically stabilized Néel order In ...

    2022

  56. [64]

    2), effectively decoupling the system into two in- dependent subsystems

    Sublattice ferromagnetism through Nagaoka mechanism att1 = 0 In thet1 = 0 limit, thet2 terms mediate hopping ex- clusively within each sublattice (indicated in red and blue in Fig. 2), effectively decoupling the system into two in- dependent subsystems. Upon doping two holes i...

  57. [65]

    This term introduces a coupling that energetically fa- vors specific spin alignments, thereby stabilizing antifer- romagnetic order

    Antiferromagnetic order through inter-sublattice hoppingt1 We now discuss how a small nearest-neighbor hopping amplitude t1 perturbatively lifts the degeneracy among different relative spin orientations of the two sublattices. This term introduces a coupling that energetically...

  58. [66]

    This implies that the lowest-energy state resides in the Stotal = 0 sector, where S1 and S2 are aligned antiparallel to form a singlet ground state

    (A6) Here,S1 andS2 denote the total spins of the two sublat- tices, with equal magnitude, andc> 0 is a positive con- stant. This implies that the lowest-energy state resides in the Stotal = 0 sector, where S1 and S2 are aligned antiparallel to form a singlet ground state. The ...

  59. [67]

    Robustness of the kinetically stabilized Néel order for finitet1/t2 On top of the perturbative wavefunction approach, we now verify the stability of the kinetically stabilized Néel order at larget1 regime through numerical exact diag- onalization using the XDiag and QuSpin pac...

  60. [68]

    In this regime, the nearest-neighbor hoppingt1 vanishes, and the Hamilto- nian features Ising-type spin interactions: H = −t2 X ⟨⟨jl⟩⟩,σ c† jσclσ +h.c

    Hamiltonian and wavefunction structure Building on our previous kinetic magnetic order anal- ysis in the infinite-U limit with smallλ, we now turn to the exactly solvable limitλ = ∆ = 0. In this regime, the nearest-neighbor hoppingt1 vanishes, and the Hamilto- nian features Is...

  61. [69]

    By solving the eigenvalue equation Eq

    Pairing symmetry and Cooper pair wavefunction Analyzing the two-hole Cooper pair wavefunction yields essential insights into the pairing symmetry and spatial structure in the(λ, ∆) = (0, 0) limit. By solving the eigenvalue equation Eq. (B4) for various center-of- mass momentaK...

  62. [70]

    Continuum limit analysis and binding energy To further understand the pairing structure, we con- sider the continuum limit analysis, which reveals crucial properties of bound states in the (λ, ∆) = (0 , 0) limit. The continuum approximation is particularly effective when the C...

  63. [71]

    Understanding these effects is cru- cial for correctly interpreting our numerical results and extrapolating to the thermodynamic limit

    Finite size effects Finite-size effects significantly impact both the spatial profile of Cooper pairs and their binding energies in nu- merical simulations. Understanding these effects is cru- cial for correctly interpreting our numerical results and extrapolating to the therm...

  64. [72]

    Motivation and methodology To capture the essential physics of antiferromagnetic polarons as pairing glue, we develop a targeted Hilbert space truncation strategy that selectively incorporates spin fluctuations in the vicinity of doped holes. This strategy enables exact diagon...

  65. [73]

    thresh- old distance

    Single-hole basis construction Our Hilbert space construction begins with a system- atic methodology for the single-hole case, which lays the foundation for addressing the complexities of the two- hole problem. The goal is to balance computational efficiency with physical accu...

  66. [74]

    threshold distance

    Two-hole basis construction We now systematically extend the Hilbert space con- structionmethoddevelopedforthesingle-holecasetothe two-hole scenario, enabling unbiased energy comparisons across a wide range of hole configurations. While the construction follows similar guiding...

  67. [75]

    Momentum sector for superconducting gap We demonstrate that the careful selection of momen- tum sectors plays a crucial role in suppressing finite-size effects in superconducting gap calculations. By system- atically comparing ground and excited states across dif- ferent momen...

  68. [76]

    Pairing symmetry We identify the pairing symmetry of the superconduct- ing ground state by systematically analyzing pair–pair correlation functions across different bond orientations. This approach allows us to distinguish between different pairing symmetries —such ass-wave an...

  69. [8000]

    This mild and systematic bias originates from the entropic preference for more localized hole configurations in DMRG calculations

    The two datasets show excellent agreement, with smaller bond dimensions tending to modestly overesti- mate the pairing strength. This mild and systematic bias originates from the entropic preference for more localized hole configurations in DMRG calculations. Finally, we bench...

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