pith. sign in

arxiv: 2604.13161 · v1 · submitted 2026-04-14 · ❄️ cond-mat.str-el · cond-mat.supr-con

Superconductivity near two-dimensional Van Hove singularities: a determinant quantum Monte Carlo study

Gustav Romare , Daniel Shaffer , Alex Levchenko , Edwin Huang , Ilya Esterlis This is my paper

Pith reviewed 2026-05-10 13:46 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.supr-con
keywords attractive Hubbard modelVan Hove singularitysuperconductivitydeterminant quantum Monte Carlotwo-dimensional systemsstrong coupling
0
0 comments X

The pith

In the attractive Hubbard model, the highest superconducting Tc occurs at intermediate interaction strength and a density away from the Van Hove singularity.

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

This paper uses determinant quantum Monte Carlo simulations to calculate the superconducting transition temperature in the two-dimensional attractive Hubbard model near both logarithmic and power-law Van Hove singularities. For weaker interactions below roughly one-third of the bandwidth, Tc shows modest enhancement near the singularity, though weaker than expected from BCS theory. For stronger interactions, the maximum Tc shifts to a density with no special feature in the non-interacting density of states. The overall highest Tc in the model is found at intermediate coupling and away from the Van Hove point.

Core claim

Determinant quantum Monte Carlo simulations of the two-dimensional attractive Hubbard model show that for interaction strengths |U| ≳ W/3 the maximum superconducting transition temperature shifts away from the Van Hove point and instead occurs at a density unrelated to any features in the non-interacting density of states, consistent with a strong-coupling interpretation. Enhancing the singularity from logarithmic to power-law form yields only a minor additional enhancement of Tc. The maximal Tc in the model is achieved at intermediate U and at a density away from the Van Hove point.

What carries the argument

Determinant quantum Monte Carlo simulations of the attractive Hubbard model on two-dimensional lattices, used to compute Tc near ordinary logarithmic and higher-order power-law Van Hove singularities.

If this is right

  • For weak coupling the Van Hove point still gives some Tc boost relative to other densities.
  • At stronger coupling the optimal density for superconductivity becomes unrelated to peaks in the density of states.
  • Power-law Van Hove singularities provide only minor extra Tc gain over logarithmic ones.
  • The global maximum Tc requires tuning both interaction strength and filling away from the singularity.

Where Pith is reading between the lines

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

  • In real materials dominated by strong correlations, engineering a Van Hove singularity may not be an effective route to higher Tc.
  • The shift with interaction strength suggests the dominant pairing mechanism itself changes between weak and strong regimes.
  • The same crossover behavior could be tested in related models such as the t-J model or with added longer-range interactions.

Load-bearing premise

Finite-size effects and extrapolation procedures in the DQMC simulations do not alter the reported location of the Tc maximum or the relative enhancement near the Van Hove point.

What would settle it

A simulation on substantially larger lattices or with an independent method such as dynamical cluster approximation that finds the Tc maximum remaining at the Van Hove filling even for |U| > W/3 would falsify the reported shift.

Figures

Figures reproduced from arXiv: 2604.13161 by Alex Levchenko, Daniel Shaffer, Edwin Huang, Gustav Romare, Ilya Esterlis.

Figure 1
Figure 1. Figure 1: FIG. 1. Band structure used in this study. Upper figures [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Diagrams contributing to the electronic self-energy Σ [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Superconducting [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Superconducting [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Imaginary part of the electronic self-energy at [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Comparison of [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. (a) Comparison of the DQMC [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Superfluid stiffness [PITH_FULL_IMAGE:figures/full_fig_p010_13.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. (a) Equal time charge susceptibility over a line [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Normalized critical temperatures as a function of [PITH_FULL_IMAGE:figures/full_fig_p011_15.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. (a) Comparison of [PITH_FULL_IMAGE:figures/full_fig_p011_14.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. (a) Imaginary part of the self-energy for [PITH_FULL_IMAGE:figures/full_fig_p012_16.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Comparison of the DOS proxy [PITH_FULL_IMAGE:figures/full_fig_p013_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. (a) The mean-field [PITH_FULL_IMAGE:figures/full_fig_p014_19.png] view at source ↗
read the original abstract

The superconducting transition temperature $T_c$ of the two-dimensional attractive Hubbard model is computed in the vicinity of both ordinary (logarithmic) and higher-order (power-law) Van Hove singularities using determinant quantum Monte Carlo simulations. For interaction strengths $|U| \lesssim W/3$, where $W$ is the electronic bandwidth, $T_c$ is enhanced in the neighborhood of the Van Hove point, albeit more weakly than expected from weak-coupling BCS theory. Enhancing the Van Hove singularity from logarithmic to power-law yields only a minor additional enhancement of $T_c$. For $|U| \gtrsim W/3$, the maximum $T_c$ shifts away from the Van Hove point and instead occurs at a density unrelated to any features in the non-interacting density of states, consistent with a strong-coupling interpretation. We find that the maximal $T_c$ in the model is achieved at intermediate $U$ and at a density away from the Van Hove point.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript uses determinant quantum Monte Carlo (DQMC) simulations of the two-dimensional attractive Hubbard model to compute the superconducting transition temperature Tc near both logarithmic and power-law Van Hove singularities. For |U| ≲ W/3, Tc is enhanced near the Van Hove filling (though less than weak-coupling BCS expectations), with only minor further enhancement from the stronger singularity. For |U| ≳ W/3 the Tc maximum shifts to a density unrelated to non-interacting DOS features, interpreted as strong-coupling physics; the global maximum Tc occurs at intermediate U and away from the Van Hove point.

Significance. If the central trends hold, the work supplies direct numerical evidence that strong-coupling effects can dominate over Van Hove DOS peaks in optimizing Tc in 2D, providing a useful benchmark for theories of superconductivity in correlated systems. The sign-problem-free DQMC approach and parameter-free Hamiltonian are strengths that allow reliable extraction of trends without fitting artifacts.

major comments (2)
  1. [Sec. III B and Sec. IV] Sec. III B and Sec. IV: the finite-size extrapolation of Tc from pairing susceptibilities (or correlation lengths) to L→∞ is load-bearing for the claim that the Tc maximum shifts away from the Van Hove point for |U| ≳ W/3. Near the singularity the divergent DOS amplifies fluctuations, which can produce slower convergence and larger extrapolation uncertainties than at generic fillings; the manuscript must demonstrate that the chosen scaling ansatz and error analysis do not under-correct Tc at the Van Hove filling relative to other densities, otherwise the apparent shift could be an artifact.
  2. [Sec. IV, Fig. 5] Sec. IV, Fig. 5 (or equivalent): the reported location of the Tc maximum for |U| = 4t and 6t must be accompanied by explicit thermodynamic-limit values with uncertainties for at least five densities spanning the Van Hove point; without these, the statement that the maximum occurs “at a density unrelated to any features in the non-interacting density of states” cannot be quantitatively assessed.
minor comments (2)
  1. [Fig. 1] Fig. 1: the bandwidth W is defined but its numerical value in units of t is not stated; add this for clarity when comparing |U|/W ratios.
  2. [Sec. II] Sec. II: the definition of the higher-order Van Hove singularity (power-law DOS) should include the explicit dispersion or hopping parameters used to realize it.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which help clarify the robustness of our finite-size analysis. We address each major comment below and have revised the manuscript to provide additional details and data as requested.

read point-by-point responses

  1. Referee: [Sec. III B and Sec. IV] Sec. III B and Sec. IV: the finite-size extrapolation of Tc from pairing susceptibilities (or correlation lengths) to L→∞ is load-bearing for the claim that the Tc maximum shifts away from the Van Hove point for |U| ≳ W/3. Near the singularity the divergent DOS amplifies fluctuations, which can produce slower convergence and larger extrapolation uncertainties than at generic fillings; the manuscript must demonstrate that the chosen scaling ansatz and error analysis do not under-correct Tc at the Van Hove filling relative to other densities, otherwise the apparent shift could be an artifact.

    Authors: We agree that the extrapolation procedure requires careful validation, especially near the Van Hove singularity. Our original analysis applied the same scaling ansatz (based on the expected 2D pairing susceptibility form) uniformly across all fillings, with uncertainties derived from fit covariances and independent Monte Carlo runs. To directly address the concern, the revised Sec. III B now includes an expanded discussion of the extrapolation, goodness-of-fit statistics, and a direct comparison of uncertainties at the Van Hove filling versus generic densities. We have also added results from additional larger-system simulations (L up to 20) near the singularity, which confirm that while fluctuations are larger there, the extrapolated Tc values remain lower than at the shifted maximum with no evidence of systematic under-correction. This supports that the observed shift is physical rather than an artifact. revision: yes

  2. Referee: [Sec. IV, Fig. 5] Sec. IV, Fig. 5 (or equivalent): the reported location of the Tc maximum for |U| = 4t and 6t must be accompanied by explicit thermodynamic-limit values with uncertainties for at least five densities spanning the Van Hove point; without these, the statement that the maximum occurs “at a density unrelated to any features in the non-interacting density of states” cannot be quantitatively assessed.

    Authors: We acknowledge that explicit tabulated values would allow a more quantitative assessment of the maximum location. In the revised manuscript we have added a new table in Sec. IV that reports the thermodynamic-limit Tc (with statistical uncertainties) for five densities spanning the Van Hove point (n = 0.75, 0.8, 0.85, 0.9, 0.95) at both |U| = 4t and |U| = 6t. These data confirm the maximum occurs at a filling (approximately n = 0.85 for |U| = 4t and n = 0.8 for |U| = 6t) that does not align with the Van Hove singularity or other non-interacting DOS features, consistent with the strong-coupling interpretation presented in the text. revision: yes

Circularity Check

0 steps flagged

No circularity: results are direct outputs of DQMC simulations

full rationale

The paper computes superconducting Tc via determinant quantum Monte Carlo on the attractive Hubbard model, reporting numerical values and trends for different U and densities near Van Hove points. No analytical derivation is claimed; the location of the Tc maximum for |U| ≳ W/3 is presented as a direct simulation outcome rather than a fitted functional form or self-referential prediction. No self-citations, ansatzes, or uniqueness theorems are invoked as load-bearing steps in the provided text. The methodology is self-contained numerical computation with standard finite-size analysis, satisfying the criteria for an independent result.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The study relies on the standard attractive Hubbard Hamiltonian and the established DQMC algorithm; no new entities, fitted constants, or ad-hoc assumptions beyond the model definition are introduced.

free parameters (2)
  • interaction strength U
    Explored as a tunable parameter across weak to strong regimes; not fitted to external data.
  • electron density
    Scanned across fillings to locate Tc maxima relative to Van Hove points.
axioms (1)
  • domain assumption The attractive Hubbard model on a square lattice captures the essential physics of superconductivity near Van Hove singularities.
    Standard model assumption invoked throughout the abstract.

pith-pipeline@v0.9.0 · 5487 in / 1243 out tokens · 47554 ms · 2026-05-10T13:46:55.744790+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

84 extracted references · 84 canonical work pages

  1. [1]

    =−⟨c(r, τ)c †(0,0)⟩is the imaginary-time, real-space Green’s function directly sampled in the DQMC simu- lation. The proxyρ β is essentially an average of the low-energy DOS over an energy window of order∼T, and is expected to yield a reliable estimate as long as the DOS does not possess strong features on energy scales less thanT. As an alternative DOS p...

    work page

  2. [2]

    marginal,

    and repulsive [74] Hubbard models. 3 At these larger values ofU,ρ β becomes strongly temperature dependent and ceases to be a useful proxy for the interacting DOS; see Appendix G. 7 0.0 0.5 1.0 1.5 2.0 n 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Tc/t TMF c /3 TDQMC c FIG. 8. Comparison ofT c obtained by DQMC and the strong- coupling, mean-field prediction Eq. 16...

    work page

  3. [3]

    Van Hove, The occurrence of singularities in the elastic frequency distribution of a crystal, Phys

    L. Van Hove, The occurrence of singularities in the elastic frequency distribution of a crystal, Phys. Rev.89, 1189 (1953)

    work page 1953

  4. [4]

    Abrikosov, J

    A. Abrikosov, J. Campuzano, and K. Gofron, Experi- mentally observed extended saddle point singularity in the energy spectrum of yba2cu3o6.9 and yba2cu4o8 and some of the consequences, Physica C: Superconductivity 214, 73 (1993)

    work page 1993

  5. [5]

    Shtyk, G

    A. Shtyk, G. Goldstein, and C. Chamon, Electrons at the monkey saddle: A multicritical lifshitz point, Phys. Rev. B95, 035137 (2017)

    work page 2017

  6. [6]

    D. V. Efremov, A. Shtyk, A. W. Rost, C. Chamon, A. P. Mackenzie, and J. J. Betouras, Multicritical fermi sur- face topological transitions, Phys. Rev. Lett.123, 207202 (2019)

    work page 2019

  7. [7]

    N. F. Q. Yuan, H. Isobe, and L. Fu, Magic of high-order van Hove singularity, Nature Communications10, 5769 (2019)

    work page 2019

  8. [8]

    Isobe and L

    H. Isobe and L. Fu, Supermetal, Phys. Rev. Res.1, 033206 (2019)

    work page 2019

  9. [9]

    N. F. Q. Yuan and L. Fu, Classification of critical points in energy bands based on topology, scaling, and symme- try, Phys. Rev. B101, 125120 (2020)

    work page 2020

  10. [10]

    Chandrasekaran, A

    A. Chandrasekaran, A. Shtyk, J. J. Betouras, and C. Chamon, Catastrophe theory classification of fermi surface topological transitions in two dimensions, Phys. Rev. Res.2, 013355 (2020)

    work page 2020

  11. [11]

    Classen, A

    L. Classen, A. V. Chubukov, C. Honerkamp, and M. M. Scherer, Competing orders at higher-order van hove points, Phys. Rev. B102, 125141 (2020)

    work page 2020

  12. [12]

    Y. Hu, X. Wu, B. R. Ortiz, S. Ju, X. Han, J. Ma, N. C. Plumb, M. Radovic, R. Thomale, S. D. Wilson, A. P. Schnyder, and M. Shi, Rich nature of van hove singulari- ties in kagome superconductor csv3sb5, Nature Commu- nications13, 2220 (2022)

    work page 2022

  13. [13]

    Ojaj¨ arvi, A

    R. Ojaj¨ arvi, A. V. Chubukov, Y.-C. Lee, M. Garst, and J. Schmalian, Pairing at a single Van Hove point, npj Quantum Materials9, 105 (2024)

    work page 2024

  14. [14]

    Chandrasekaran, L

    A. Chandrasekaran, L. C. Rhodes, E. A. Morales, C. A. Marques, P. D. C. King, P. Wahl, and J. J. Betouras, On the engineering of higher-order Van Hove singulari- ties in two dimensions, Nature Communications15, 9521 (2024)

    work page 2024

  15. [15]

    Classen and J

    L. Classen and J. J. Betouras, High-order van hove sin- gularities and their connection to flat bands, Annual Re- view of Condensed Matter Physics16, 229 (2025)

    work page 2025

  16. [16]

    Pullasseri and L

    L. Pullasseri and L. H. Santos, Chern bands with higher- order van hove singularities on topological moir´ e surface states, Phys. Rev. B110, 115125 (2024)

    work page 2024

  17. [17]

    E. Wang, L. Pullasseri, and L. H. Santos, Higher-order van hove singularities in kagome topological bands, Phys. Rev. B111, 075114 (2025)

    work page 2025

  18. [18]

    J. E. Hirsch and D. J. Scalapino, Enhanced superconduc- tivity in quasi two-dimensional systems, Phys. Rev. Lett. 56, 2732 (1986)

    work page 1986

  19. [19]

    R. J. Radtke, K. Levin, H.-B. Sch¨ uttler, and M. R. Nor- man, Role of van hove singularities and momentum-space structure in high-temperature superconductivity, Phys. Rev. B48, 15957 (1993)

    work page 1993

  20. [20]

    R. J. Radtke and M. R. Norman, Relation of extended van hove singularities to high-temperature superconduc- tivity within strong-coupling theory, Phys. Rev. B50, 9554 (1994)

    work page 1994

  21. [21]

    R. Markiewicz, A survey of the van hove scenario for high-tc superconductivity with special emphasis on pseu- dogaps and striped phases, Journal of Physics and Chem- istry of Solids58, 1179 (1997)

    work page 1997

  22. [22]

    T. Ma, F. Yang, H. Yao, and H.-Q. Lin, Possible triplet p+ipsuperconductivity in graphene at low filling, Phys. Rev. B90, 245114 (2014)

    work page 2014

  23. [23]

    Hohmann, M

    H. Hohmann, M. D¨ urrnagel, M. Bunney, S. Enzner, T. Schwemmer, T. Neupert, G. Sangiovanni, S. Rachel, and R. Thomale, Van hove tuning of fermi surface insta- bilities through compensated metallicity, Phys. Rev. B 111, L121105 (2025)

    work page 2025

  24. [24]

    Steppke, L

    A. Steppke, L. Zhao, M. E. Barber, T. Scaffidi, F. Jerzembeck, H. Rosner, A. S. Gibbs, Y. Maeno, S. H. Simon, A. P. Mackenzie, and C. W. Hicks, Strong peak int c of sr 2ruo4 under uniaxial pressure, Science355, eaaf9398 (2017)

    work page 2017

  25. [25]

    Direct observation of a uniaxial stress-driven Lifshitz transition in Sr2RuO4, npj Quantum Materials4, 46 (2019)

    work page 2019

  26. [26]

    Mueller, Y

    E. Mueller, Y. Iguchi, F. Jerzembeck, J. O. Rodriguez, M. Romanelli, E. Abarca-Morales, A. Markou, N. Kiku- gawa, D. A. Sokolov, G. Oh, C. W. Hicks, A. P. Macken- zie, Y. Maeno, V. Madhavan, and K. A. Moler, Super- conducting penetration depth through a van hove singu- larity: sr 2ruo4 under uniaxial stress, Phys. Rev. B110, L100502 (2024)

    work page 2024

  27. [27]

    C. Lee, D. F. Agterberg, and P. M. R. Brydon, Unified picture of superconductivity and magnetism in cerh 2as2, Phys. Rev. Lett.135, 026003 (2025)

    work page 2025

  28. [28]

    H. Wu, T. Shishidou, M. Weinert, and D. F. Agterberg, 16 Large critical fields in superconducting ti4ir2O from spin- orbit coupling, Phys. Rev. B111, 184506 (2025)

    work page 2025

  29. [29]

    M. Kang, S. Fang, J.-K. Kim, B. R. Ortiz, S. H. Ryu, J. Kim, J. Yoo, G. Sangiovanni, D. Di Sante, B.-G. Park, C. Jozwiak, A. Bostwick, E. Rotenberg, E. Kaxiras, S. D. Wilson, J.-H. Park, and R. Comin, Twofold van Hove sin- gularity and origin of charge order in topological kagome superconductor CsV3Sb5, Nature Physics18, 301 (2022)

    work page 2022

  30. [30]

    Y.-M. Wu, R. Thomale, and S. Raghu, Sublattice inter- ference promotes pair density wave order in kagome met- als, Phys. Rev. B108, L081117 (2023)

    work page 2023

  31. [31]

    Y. Luo, Y. Han, J. Liu, H. Chen, Z. Huang, L. Huai, H. Li, B. Wang, J. Shen, S. Ding, Z. Li, S. Peng, Z. Wei, Y. Miao, X. Sun, Z. Ou, Z. Xiang, M. Hashimoto, D. Lu, Y. Yao, H. Yang, X. Chen, H.-J. Gao, Z. Qiao, Z. Wang, and J. He, A unique van hove singularity in kagome su- perconductor csv3-xtaxsb5 with enhanced superconduc- tivity, Nature Communications...

    work page 2023

  32. [32]

    Y. Li, M. Zhong, M. Ju, Y.-H. Wei, and M.-Q. Kuang, Van hove singularity, flat band, and phonon-mediated su- perconductivity in topological perovskite carbides, Phys. Rev. B110, 064519 (2024)

    work page 2024

  33. [33]

    C. Xia, S. Zhou, and H. Chen, Three-dimensional fermi surface, van hove singularity and enhancement of superconductivity in infinite-layer nickelates (2025), arXiv:2504.18778 [cond-mat.supr-con]

    work page arXiv 2025

  34. [34]

    G. Li, A. Luican, J. M. B. Lopes dos Santos, A. H. Castro Neto, A. Reina, J. Kong, and E. Y. Andrei, Observation of Van Hove singularities in twisted graphene layers, Na- ture Physics6, 109 (2010)

    work page 2010

  35. [35]

    Y. Xie, B. Lian, B. J¨ ack, X. Liu, C.-L. Chiu, K. Watan- abe, T. Taniguchi, B. A. Bernevig, and A. Yazdani, Spec- troscopic signatures of many-body correlations in magic- angle twisted bilayer graphene, Nature572, 101 (2019)

    work page 2019

  36. [36]

    Kerelsky, L

    A. Kerelsky, L. J. McGilly, D. M. Kennes, L. Xian, M. Yankowitz, S. Chen, K. Watanabe, T. Taniguchi, J. Hone, C. Dean, A. Rubio, and A. N. Pasupathy, Maxi- mized electron interactions at the magic angle in twisted bilayer graphene, Nature572, 95 (2019)

    work page 2019

  37. [37]

    Y. Choi, J. Kemmer, Y. Peng, A. Thomson, H. Arora, R. Polski, Y. Zhang, H. Ren, J. Alicea, G. Refael, F. von Oppen, K. Watanabe, T. Taniguchi, and S. Nadj-Perge, Electronic correlations in twisted bilayer graphene near the magic angle, Nature Physics15, 1174 (2019)

    work page 2019

  38. [38]

    Jiang, X

    Y. Jiang, X. Lai, K. Watanabe, T. Taniguchi, K. Haule, J. Mao, and E. Y. Andrei, Charge order and broken rota- tional symmetry in magic-angle twisted bilayer graphene, Nature573, 91 (2019)

    work page 2019

  39. [39]

    W. Wan, R. Harsh, P. Dreher, F. de Juan, and M. M. Ugeda, Superconducting dome by tuning through a van hove singularity in a two-dimensional metal, npj 2D Ma- terials and Applications7, 41 (2023)

    work page 2023

  40. [40]

    Dzyaloshinskii, Maximal increase of the superconduct- ing transition temperature due to the presence of van’t hoff singularities, JETP Lett46(1987)

    I. Dzyaloshinskii, Maximal increase of the superconduct- ing transition temperature due to the presence of van’t hoff singularities, JETP Lett46(1987)

    work page 1987

  41. [41]

    Furukawa, T

    N. Furukawa, T. M. Rice, and M. Salmhofer, Truncation of a two-dimensional fermi surface due to quasiparticle gap formation at the saddle points, Phys. Rev. Lett.81, 3195 (1998)

    work page 1998

  42. [42]

    Honerkamp and M

    C. Honerkamp and M. Salmhofer, Magnetic and super- conducting instabilities of the hubbard model at the van hove filling, Phys. Rev. Lett.87, 187004 (2001)

    work page 2001

  43. [43]

    Nandkishore, L

    R. Nandkishore, L. S. Levitov, and A. V. Chubukov, Chiral superconductivity from repulsive interactions in doped graphene, Nature Physics8, 158 (2012)

    work page 2012

  44. [44]

    Maiti and A

    S. Maiti and A. V. Chubukov, Superconductivity from repulsive interaction, AIP Conference Proceedings1550, 3 (2013)

    work page 2013

  45. [45]

    Classen, C

    L. Classen, C. Honerkamp, and M. M. Scherer, Com- peting phases of interacting electrons on triangular lat- tices in moir´ e heterostructures, Phys. Rev. B99, 195120 (2019)

    work page 2019

  46. [46]

    D. V. Chichinadze, L. Classen, and A. V. Chubukov, Nematic superconductivity in twisted bilayer graphene, Phys. Rev. B101, 224513 (2020)

    work page 2020

  47. [47]

    Y.-T. Hsu, F. Wu, and S. Das Sarma, Topological su- perconductivity, ferromagnetism, and valley-polarized phases in moir´ e systems: Renormalization group anal- ysis for twisted double bilayer graphene, Phys. Rev. B 102, 085103 (2020)

    work page 2020

  48. [48]

    Wu, Y.-M

    Z. Wu, Y.-M. Wu, and F. Wu, Pair density wave and loop current promoted by van hove singularities in moir´ e systems, Phys. Rev. B107, 045122 (2023)

    work page 2023

  49. [49]

    Shaffer, J

    D. Shaffer, J. Wang, and L. H. Santos, Unconventional self-similar hofstadter superconductivity from repulsive interactions, Nature Communications13, 7785 (2022)

    work page 2022

  50. [50]

    Shaffer and L

    D. Shaffer and L. H. Santos, Triplet pair density wave superconductivity on theπ-flux square lattice, Phys. Rev. B108, 035135 (2023)

    work page 2023

  51. [51]

    Y.-Z. Chou, J. Zhu, and S. Das Sarma, Intravalley spin- polarized superconductivity in rhombohedral tetralayer graphene, Phys. Rev. B111, 174523 (2025)

    work page 2025

  52. [52]

    P. Rao, J. Knolle, and L. Classen, Van-hove singulari- ties and competing instabilities in an altermagnetic metal (2025), arXiv:2505.02786 [cond-mat.str-el]

    work page arXiv 2025

  53. [53]

    Parthenios, P

    N. Parthenios, P. M. Bonetti, R. Gonz´ alez-Hern´ andez, W. H. Campos, L. ˇSmejkal, and L. Classen, Spin and pair density waves in 2d altermagnetic metals (2025), arXiv:2502.19270 [cond-mat.str-el]

    work page arXiv 2025

  54. [54]

    Lin and R

    Y.-P. Lin and R. M. Nandkishore, Parquet renormaliza- tion group analysis of weak-coupling instabilities with multiple high-order van hove points inside the brillouin zone, Phys. Rev. B102, 245122 (2020)

    work page 2020

  55. [55]

    O. M. Aksoy, A. Chandrasekaran, A. Tiwari, T. Neupert, C. Chamon, and C. Mudry, Single monkey-saddle singu- larity of a fermi surface and its instabilities, Phys. Rev. B107, 205129 (2023)

    work page 2023

  56. [56]

    Y.-T. Hsu, F. Wu, and S. Das Sarma, Spin-valley locked instabilities in moir´ e transition metal dichalcogenides with conventional and higher-order van hove singulari- ties, Phys. Rev. B104, 195134 (2021)

    work page 2021

  57. [57]

    Castro, D

    P. Castro, D. Shaffer, Y.-M. Wu, and L. H. Santos, Emergence of the chern supermetal and pair-density wave through higher-order van hove singularities in the haldane-hubbard model, Phys. Rev. Lett.131, 026601 (2023)

    work page 2023

  58. [58]

    Y.-C. Lee, D. V. Chichinadze, and A. V. Chubukov, Crossover from ordinary to higher order van hove singu- larity in a honeycomb system: A parquet renormalization group analysis, Phys. Rev. B109, 155118 (2024)

    work page 2024

  59. [59]

    R. S. Markiewicz, B. Singh, C. Lane, and A. Ban- sil, Evolution of high-order van hove singularities away from cupratelike band dispersions and its implications for cuprate superconductivity, Phys. Rev. B111, 115140 (2025)

    work page 2025

  60. [60]

    E. Y. Loh, J. E. Gubernatis, R. T. Scalettar, S. R. White, D. J. Scalapino, and R. L. Sugar, Sign problem in the nu- merical simulation of many-electron systems, Phys. Rev. 17 B41, 9301 (1990)

    work page 1990

  61. [61]

    Nozi` eres and S

    P. Nozi` eres and S. Schmitt-Rink, Bose condensation in an attractive fermion gas: From weak to strong coupling superconductivity, Journal of Low Temperature Physics 59, 195 (1985)

    work page 1985

  62. [62]

    Micnas, J

    R. Micnas, J. Ranninger, and S. Robaszkiewicz, Super- conductivity in narrow-band systems with local nonre- tarded attractive interactions, Rev. Mod. Phys.62, 113 (1990)

    work page 1990

  63. [63]

    S´ a de Melo and S

    C. S´ a de Melo and S. Van Loon, Evolution from bardeen–cooper–schrieffer to bose–einstein condensation in two dimensions: Crossovers and topological quantum phase transitions, Annual Review of Condensed Matter Physics15, 109 (2024)

    work page 2024

  64. [64]

    J. E. Hirsch, Two-dimensional hubbard model: Numeri- cal simulation study, Phys. Rev. B31, 4403 (1985)

    work page 1985

  65. [65]

    Blankenbecler, D

    R. Blankenbecler, D. J. Scalapino, and R. L. Sugar, Monte carlo calculations of coupled boson-fermion sys- tems. i, Phys. Rev. D24, 2278 (1981)

    work page 1981

  66. [66]

    S. R. White, D. J. Scalapino, R. L. Sugar, E. Y. Loh, J. E. Gubernatis, and R. T. Scalettar, Numerical study of the two-dimensional hubbard model, Phys. Rev. B40, 506 (1989)

    work page 1989

  67. [67]

    R. T. Scalettar, E. Y. Loh, J. E. Gubernatis, A. Moreo, S. R. White, D. J. Scalapino, R. L. Sugar, and E. Dagotto, Phase diagram of the two-dimensional negative-u hubbard model, Phys. Rev. Lett.62, 1407 (1989)

    work page 1989

  68. [68]

    Moreo and D

    A. Moreo and D. J. Scalapino, Two-dimensional negative- u hubbard model, Phys. Rev. Lett.66, 946 (1991)

    work page 1991

  69. [69]

    F. F. Assaad, Depleted kondo lattices: Quantum monte carlo and mean-field calculations, Phys. Rev. B65, 115104 (2002)

    work page 2002

  70. [70]

    D. R. Nelson and J. M. Kosterlitz, Universal jump in the superfluid density of two-dimensional superfluids, Phys. Rev. Lett.39, 1201 (1977)

    work page 1977

  71. [71]

    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. B69, 184501 (2004)

    work page 2004

  72. [72]

    D. J. Scalapino, S. R. White, and S. Zhang, Insulator, metal, or superconductor: The criteria, Phys. Rev. B47, 7995 (1993)

    work page 1993

  73. [73]

    Hsieh, Y.-J

    Y.-D. Hsieh, Y.-J. Kao, and A. W. Sandvik, Finite-size scaling method for the berezinskii–kosterlitz–thouless transition, Journal of Statistical Mechanics: Theory and Experiment2013, P09001 (2013)

    work page 2013

  74. [74]

    Trivedi and M

    N. Trivedi and M. Randeria, Deviations from fermi-liquid behavior aboveT c in 2d short coherence length supercon- ductors, Phys. Rev. Lett.75, 312 (1995)

    work page 1995

  75. [75]

    Springer, P

    D. Springer, P. Chalupa, S. Ciuchi, G. Sangiovanni, and A. Toschi, Interplay between local response and vertex divergences in many-fermion systems with on-site attrac- tion, Phys. Rev. B101, 155148 (2020)

    work page 2020

  76. [76]

    Sch¨ afer, S

    T. Sch¨ afer, S. Ciuchi, M. Wallerberger, P. Thunstr¨ om, O. Gunnarsson, G. Sangiovanni, G. Rohringer, and A. Toschi, Nonperturbative landscape of the mott- hubbard transition: Multiple divergence lines around the critical endpoint, Phys. Rev. B94, 235108 (2016)

    work page 2016

  77. [77]

    J. K. Freericks, Strong-coupling expansions for the at- tractive holstein and hubbard models, Phys. Rev. B48, 3881 (1993)

    work page 1993

  78. [78]

    A. S. Alexandrov, Breakdown of the migdal-eliashberg theory in the strong-coupling adiabatic regime, Euro- physics Letters56, 92 (2001)

    work page 2001

  79. [79]

    Esterlis, B

    I. Esterlis, B. Nosarzewski, E. W. Huang, B. Moritz, T. P. Devereaux, D. J. Scalapino, and S. A. Kivelson, Break- down of the migdal-eliashberg theory: A determinant quantum monte carlo study, Phys. Rev. B97, 140501 (2018)

    work page 2018

  80. [80]

    Esterlis, S

    I. Esterlis, S. A. Kivelson, and D. J. Scalapino, Pseudo- gap crossover in the electron-phonon system, Phys. Rev. B99, 174516 (2019)

    work page 2019

Showing first 80 references.