Pith. sign in

REVIEW 2 major objections 5 minor 61 references

Magnetic and charge susceptibilities in the half-filled triangular lattice Hubbard model

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read Strong spin fluctuations at the K point exist in both the Mott insulator and the metallic phase of the half-filled triangular Hubbard model, moving to higher energy as the interaction weakens.

desk verdict A transparent DF study of triangular-lattice spin and charge response whose headline metallic-phase spin-fluctuation result is plausible but quantitatively unverified; worth refereeing. read the letter →

arxiv 1908.10748 v1 pith:YAXNRDSU submitted 2019-08-28 cond-mat.str-el

Shaozhi Li , Emanuel Gull This is my paper · ORCID
classification cond-mat.str-el
keywords triangularlatticeHubbardmodeldualfermionapproximationspinsusceptibility120-degreeantiferromagneticorderMottmetal-insulatorcrossoverspin-latticerelaxationchargeneutronspectroscopy
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

The paper aims to establish that the half-filled triangular-lattice Hubbard model develops strong momentum- and energy-resolved spin fluctuations at the K point, the 120-degree antiferromagnetic wavevector, not only in the Mott insulating regime but also on the metallic side of the metal-insulator crossover. Using the ladder dual fermion approximation, the authors compute static and dynamic spin and charge susceptibilities at $T=t/6$ for $U=6t$, $8.2t$, and $12t$, and find that K-point spin fluctuations persist at $U=6t$--$7t$ while their characteristic energy rises as $U$ decreases. If the claim holds, the magnetic response of the model evolves continuously through the crossover, and spin-model descriptions that apply only at large $U$ miss an entire metallic regime of strong magnetic correlations. The paper also connects these spectra to inelastic neutron scattering on Ba$_8$CoNb$_6$O$_{24}$ and to NMR relaxation measurements on an organic triangular compound, and presents charge susceptibilities as predictions for momentum-resolved electron-loss spectroscopy.

What carries the argument

The load-bearing object is the two-particle magnetic susceptibility $\chi_m(\mathbf{q},\omega)$ resolved on a $24\times24$ momentum grid of the triangular Brillouin zone, computed in the ladder dual fermion approximation, a diagrammatic extension of dynamical mean-field theory that keeps local correlations nonperturbative and adds nonlocal spin and charge correlations at the ladder level. The K point, the corner of the hexagonal Brillouin zone, is the wavevector conjugate to the 120-degree antiferromagnetic spin pattern, so the location and energy of the peak in $\chi_m(\mathbf{K},\omega)$ diagnose the ordering tendency. The same two-particle machinery produces the spin-lattice relaxation rate and the bare-bubble comparison that exposes the role of vertex corrections. The authors stress that total spin and charge conservation are violated at the $\Gamma$ point in this approximation, producing spurious nonzero $\Gamma$-point excitations.

What would settle it

Compute the dynamic magnetic susceptibility at $U=6t$ and $7t$, $T=t/6$, with an unbiased method that does not rely on the dual fermion truncation, for example exact diagonalization on the largest accessible cluster or another controlled cluster method; if the K-point peak of $\mathrm{Im}\,\chi_m(\mathbf{K},\omega)$ disappears or becomes no stronger than the bare-bubble response while the density of states still shows a metal, the paper's central claim is refuted. Experimentally, momentum-resolved inelastic neutron scattering on a metallic half-filled triangular compound with $U$ near the crossover should show a resolvable K-point spin excitation above the single-particle continuum; its absence would falsify the claim.

Watch

Extended reading notes

Core claim

At $T=t/6$ the static magnetic susceptibility $\chi_m(\mathbf{q},0)$ shows a dominant peak at the K point for $U=12t$, signalling incipient 120-degree antiferromagnetic order. The dynamic susceptibility shows that this K-point spin excitation persists at $U=8.2t$ and $U=6t$, but moves to higher energy; the maximum intensity at the K point grows slowly between $U=6t$ and $7t$ and rapidly beyond, while the density of states at the Fermi level shows the system is still metallic at $U=7t$. The authors conclude that strong spin fluctuations begin to condense at the K point around $U\sim 7t$ inside the metallic phase. The spin-lattice relaxation rate $(T_1T)^{-1}$ rises with $U$, approaching magnetic-order behaviour near $T\approx0.125t$ at $U=12t$, and the computed neutron spectra at $U=12t$ reproduce the K-point intensity pattern seen in Ba$_8$CoNb$_6$O$_{24}$ when $t=3$ meV. Charge susceptibilities are suppressed by $U$, show uniform charge response in the metal, and require vertex corrections beyond the bare bubble.

Load-bearing premise

The entire result rests on the ladder dual fermion approximation being accurate enough in momentum-resolved magnetic response at $T=t/6$; the paper itself calls this approximation 'uncontrolled in practice', and known momentum-dependent errors such as the spurious $\Gamma$-point response mean the metallic K-point fluctuations could in principle be an artifact.

Editorial extensions

If this is right

  • The metal at $U\lesssim8t$ already carries incipient 120-degree antiferromagnetic correlations, so the magnetic response does not switch on abruptly at the Mott transition; it strengthens continuously as $U$ grows.
  • The spin-excitation energy at the K point drops sharply between $U=6t$ and $7t$ while the system remains metallic, locating the onset of strong K-point fluctuations inside the metallic phase rather than at the insulator boundary.
  • At $U=12t$, the computed neutron scattering pattern compares well with Ba$_8$CoNb$_6$O$_{24}$, and the Hubbard model is argued to be a more appropriate starting point than a Heisenberg model, which only becomes equivalent for $U>20t$.
  • The temperature dependence of $(T_1T)^{-1}$ for $U=6t$, $8.2t$, and $12t$ tracks the pressure dependence seen in $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$, suggesting interaction strength plays the role of pressure.
  • The momentum-resolved charge susceptibility in the metal is concentrated at the Brillouin-zone boundary at high energy and at the zone center statically, giving a concrete prediction for electron-energy-loss measurements.

Reading between the lines

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

  • If K-point spin fluctuations persist into the metal, then transport quantities such as the resistivity or the optical scattering rate should show signatures of a finite magnetic correlation length that grows as $U$ approaches the crossover; the paper does not compute these, but they are direct consequences of the susceptibility it reports.
  • The spurious $\Gamma$-point intensity in the dual fermion results suggests the quantitative energy scale of the metallic K-point fluctuations may shift under a more accurate method; a benchmark against exact diagonalization on small clusters at the same temperature would separate the physical peak from the approximation artifact.
  • The collapse of the K-point excitation energy between $U=6t$ and $7t$ resembles the behavior one would expect if a broad crossover separates a weakly correlated metal from a spin-fluctuation-dominated metal; identifying whether the associated length scale diverges would require larger clusters and lower temperatures.
  • Because the Heisenberg mapping fails below $U\sim20t$, effective exchange couplings extracted by fitting spin models to neutron data on correlated triangular materials may be systematically biased; re-fitting with the Hubbard model at finite $U$ could change the inferred $J$ values.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The manuscript studies the half-filled triangular-lattice Hubbard model at T=t/6 using the ladder dual fermion approximation with maximum-entropy analytic continuation. It presents momentum- and energy-resolved spin and charge susceptibilities for U=6t (metal), U=8.2t (crossover), and U=12t (insulator). The central claim is that strong K-point spin fluctuations corresponding to 120-degree antiferromagnetic fluctuations exist not only in the insulator but also in the metallic phase, moving to higher energy as U decreases, and that they begin to condense around U=7t. The paper also presents simulated neutron spectra, spin-lattice relaxation rates, comparisons to Ba8CoNb6O24 and κ-(ET)2Cu2(CN)3, and charge susceptibilities relevant to momentum-resolved electron-loss spectroscopy.

Significance. The metallic-phase persistence of K-point spin fluctuations and their evolution across the metal-insulator crossover would be a useful result beyond the usual strong-coupling spin-model description, and the momentum-resolved spectra are valuable for interpreting neutron and NMR experiments on triangular compounds. The paper is commendably transparent: it explicitly states that the ladder DF approximation is uncontrolled in practice, acknowledges the spurious nonzero Gamma-point spin and charge excitations, identifies the energy-scale uncertainty in the Ba8CoNb6O24 comparison, and includes a supplementary exact-diagonalization check of the Hubbard versus Heisenberg spin response. If the central crossover claim is supported by an additional cross-check, the paper would make a solid contribution; currently the evidence for that claim is not quantitatively established.

major comments (2)
  1. [Method; Figs. 1 and 2] The metallic-phase part of the central claim, namely that strong K-point spin fluctuations persist into the metal and condense around U=7t, rests solely on the ladder dual fermion susceptibility, which the Method section describes as 'uncontrolled in practice'. The only cited benchmark, Ref. 49, is for the square lattice and demonstrates momentum- and interaction-dependent scaling effects; no triangular-lattice benchmark is provided. Because the same calculation produces the acknowledged spurious nonzero spin and charge excitations at Gamma (Fig. 1(d)-(f); Fig. 5(d)-(f)), the K-point result is not protected by a conservation law. I therefore cannot determine whether the drop in omega_m(K) between U=6t and U=7t is physical or an artifact of the vertex approximation. A concrete cross-check at one metallic U, such as cluster DMFT, a finite-size QMC susceptibility, or a quantitative transfer of the Ref. 49 error estimates to the triangular lattice, is needed to support the central claim.
  2. [Fig. 2 and surrounding text] The claim that spin fluctuations 'start to condense' around U=7t is based on omega_m(K), which is the peak position of Im chi_m(K,omega) obtained from maximum-entropy analytic continuation and is shown without error bars. The sharp drop between U=6t and U=7t is a relatively small energy shift on the scale of the spectra, and MaxEnt peak positions carry systematic uncertainty from the choice of default model and from Monte Carlo noise. Please provide uncertainty estimates, for example by varying the MaxEnt default model or bootstrap resampling the raw QMC data, or alternatively phrase the condensation claim more cautiously as a qualitative observation.
minor comments (5)
  1. [Supplement, Fig. S3 caption] The caption contains a typo: 'pannel' should be 'panel'; in the supplement text 'To valid this simplification' should read 'To validate this simplification'.
  2. [Supplement, bare susceptibility discussion] The supplement refers to 'Fig. 1(b)' for spin excitations and 'Fig. 4(b)' for charge excitations in the main text; the correct references appear to be Fig. 1(d)-(f) and Fig. 5(d)-(f), respectively.
  3. [Main text, Fig. 5 discussion] The phrase 'is invisible in the insulator (U=12t)' is ambiguous; the charge susceptibility is small but not necessarily zero, so 'suppressed below the scale of the plot' or 'negligible' would be more precise.
  4. [Fig. 2(a)] The density of states is plotted together with omega_m(K) but the DOS axis is not labeled in the panel; the caption should state explicitly which curve and scale refer to the DOS, as the right axis appears unlabeled.
  5. [Supplement, author affiliation line] The affiliation line on the supplementary material contains a formatting error: '1,2Center for Computational Quantum Physics' duplicates the numbering and should be cleaned up.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the K-point spin-fluctuation result is a direct DF susceptibility output; the only fit is a global energy scale for experiment comparison.

full rationale

The paper's central claim, that strong K-point spin fluctuations exist in both the metallic and insulating regimes of the half-filled triangular Hubbard model, is a direct numerical output of the ladder dual-fermion susceptibility calculation. No parameter is fitted to the K-point response; the susceptibility is computed from the model Hamiltonian with U and T chosen and t=1. The only fit in the paper is the global hopping scale t=3 meV used for the Ba8CoNb6O24 neutron-scattering comparison (Fig. 3), and this scale does not feed back into the Hubbard-model calculation or into the metallic-phase K-point result. The comparison between Hubbard and Heisenberg models in the supplement is a validation benchmark, not an input to the susceptibility computation. Reference [49], which includes the present authors, is a square-lattice benchmark invoked to support the overall momentum dependence of the DF approximation; it is not used as a uniqueness theorem and does not define the susceptibility by construction. The acknowledged approximations and artifacts, such as the nonzero Gamma-point spin and charge excitations and the statement that DF is 'uncontrolled in practice,' are accuracy and correctness limitations rather than circularity. Accordingly, no circular step can be identified from the quoted text, and the score is 0.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central spin-fluctuation claim arises directly from the DF calculation with model parameters U and T; no extra entities are invented. The only fit is the energy scale t for the experimental comparison, which does not feed back into the model. The main burden is the uncontrolled DF approximation and the MaxEnt continuation, not circular fitting.

free parameters (2)
  • t (energy scale for Ba8CoNb6O24 comparison) = 3 meV
    Fitted to match the experimental neutron scattering energy scale in Fig. 3. This only affects the experimental comparison, not the central model predictions.
  • Interaction strengths U = 6t, 8.2t, 12t (plus 7t for the condensation onset)
    Chosen by hand to represent metallic, crossover, and insulating regimes, based on the transition at U~9.5t. They are model inputs, not fitted to the target susceptibilities.
assumptions (3)
  • domain assumption The half-filled single-orbital nearest-neighbor Hubbard model on a triangular lattice captures the low-energy physics of Ba8CoNb6O24 and kappa-(ET)2Cu2(CN)3.
    Used to justify the comparison of DF spectra to experiments on these materials; the Hubbard model is standard but ignores real-material details such as lattice distortions and longer-range hoppings.
  • ad hoc to paper The ladder dual fermion approximation yields accurate two-particle response functions on the triangular lattice at T=t/6.
    The paper calls DF 'uncontrolled in practice' (Sec. Method) and reports spurious nonzero Gamma-point spin and charge excitations, so the accuracy of the two-particle spectra is an unverified premise that the central claim depends on.
  • standard math Maximum entropy analytic continuation reliably reconstructs real-frequency spectra from Matsubara data.
    Used via the ALPS implementation; standard, but known to have model dependence, especially for broad spectral features, and no error bars are provided here.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Magnetic and charge susceptibilities in the half-filled triangular lattice Hubbard model." pith.science (2026). https://pith.science/paper/YAXNRDSU

@misc{pith2026190810748,
  author       = {Pith},
  title        = {Pith review of: Magnetic and charge susceptibilities in the half-filled triangular lattice Hubbard model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YAXNRDSU}},
  note         = {Machine review of arXiv:1908.10748}
}
abstract

We study magnetic and charge susceptibilities in the half-filled two-dimensional triangular Hubbard model within the dual fermion approximation in the metallic, Mott insulating, and crossover regions of parameter space. In the \textcolor{black}{insulating state}, we find strong spin fluctuations at the K point at low energy corresponding to the \textcolor{black}{120$^{\circ}$} antiferromagnetic order. These spin fluctuations persist into the metallic phase and move to higher energy. We also present data for simulated neutron spectroscopy and \textcolor{black}{spin-lattice} relaxation times, and perform direct comparisons to inelastic neutron spectroscopy experiments on the triangular material Ba$_8$CoNb$_6$O$_{24}$ and to the relaxation times on $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$. Finally, we present charge susceptibilities in different areas of parameter space, which should correspond to momentum-resolved electron-loss spectroscopy measurements on triangular compounds.

Figures

Figures reproduced from arXiv: 1908.10748 by the authors.

Figure 1
Figure 1. FIG. 1. Panels (a), (b), and (c): Static magnetic susceptibility in the momentum space, [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Panel (a): The spin excitation energy [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Panel (a): Spin susceptibility Im [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Panels (a), (b), and (c): Static charge susceptibility in momentum space, [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

61 extracted references · 53 canonical work pages

  1. [1]

    Shimizu, K

    Y. Shimizu, K. Miyagawa, K. Kanoda, M. Maesato, and G. Saito, Phys. Rev. Lett. 91, 107001 (2003)

    2003

  2. [2]

    Kurosaki, Y

    Y. Kurosaki, Y. Shimizu, K. Miyagawa, K. Kanoda, and G. Saito, Phys. Rev. Lett. 95, 177001 (2005)

    work page 2005

  3. [3]

    T. Itou, A. Oyamada, S. Maegawa, M. Tamura, and R. Kato, Journal of Physics: Condensed Matter 19, 145247 (2007)

    work page 2007

  4. [4]

    Yamashita, N

    M. Yamashita, N. Nakata, Y. Senshu, M. Nagata, H. M. Yamamoto, R. Kato, T. Shibauchi, and Y. Matsuda, Science 328, 1246 (2010)

    work page 2010

  5. [5]

    Yamashita, T

    S. Yamashita, T. Yamamoto, Y. Nakazawa, M. Tamura, and R. Kato, Nature Communications 2, 275 EP (2011)

    work page 2011

  6. [6]

    Isono, H

    T. Isono, H. Kamo, A. Ueda, K. Takahashi, M. Ki- mata, H. Tajima, S. Tsuchiya, T. Terashima, S. Uji, and H. Mori, Phys. Rev. Lett. 112, 177201 (2014)

    work page 2014

  7. [7]

    Y. Zhou, K. Kanoda, and T.-K. Ng, Rev. Mod. Phys. 89, 025003 (2017)

    2017

  8. [8]

    Shirakawa, T

    T. Shirakawa, T. Tohyama, J. Kokalj, S. Sota, and S. Yunoki, Phys. Rev. B 96, 205130 (2017)

    2017

Show all 61 references
  1. [9]

    R. Rawl, L. Ge, H. Agrawal, Y. Kamiya, C. R. Dela Cruz, N. P. Butch, X. F. Sun, M. Lee, E. S. Choi, J. Oitmaa, C. D. Batista, M. Mourigal, H. D. Zhou, and J. Ma, Phys. Rev. B 95, 060412(R) (2017)

    2017

  2. [10]

    Pustogow, M

    A. Pustogow, M. Bories, A. Lhle, R. Rsslhuber, E. Zhukova, B. Gorshunov, S. Tomi, J. A. Schlueter, R. Hbner, T. Hiramatsu, Y. Yoshida, G. Saito, R. Kato, T. H. Lee, V. Dobrosavljevi, S. Fratini, and M. Dressel, Nature Materials 17, 773 (2018)

    2018

  3. [11]

    Koretsune, Y

    T. Koretsune, Y. Motome, and A. Furusaki, Journal of the Physical Society of Japan 76, 074719 (2007)

    2007

  4. [12]

    R. T. Clay, H. Li, and S. Mazumdar, Phys. Rev. Lett. 101, 166403 (2008)

    2008

  5. [13]

    Kokalj and R

    J. Kokalj and R. H. McKenzie, Phys. Rev. Lett. 110, 206402 (2013)

    2013

  6. [14]

    Watanabe, H

    T. Watanabe, H. Yokoyama, Y. Tanaka, and J.-i. In- oue, Journal of the Physical Society of Japan 75, 074707 (2006)

    2006

  7. [15]

    Watanabe, H

    T. Watanabe, H. Yokoyama, Y. Tanaka, and J. Inoue, Phys. Rev. B 77, 214505 (2008)

    2008

  8. [16]

    L. F. Tocchio, C. Gros, R. Valent´ ı, and F. Becca, Phys. Rev. B 89, 235107 (2014)

    2014

  9. [17]

    L. F. Tocchio, H. Feldner, F. Becca, R. Valent´ ı, and C. Gros, Phys. Rev. B 87, 035143 (2013)

    2013

  10. [18]

    Sahebsara and D

    P. Sahebsara and D. S´ en´ echal, Phys. Rev. Lett. 100, 136402 (2008)

    2008

  11. [19]

    Yamada, Phys

    A. Yamada, Phys. Rev. B 89, 195108 (2014)

    2014

  12. [20]

    Misumi, T

    K. Misumi, T. Kaneko, and Y. Ohta, Phys. Rev. B 95, 075124 (2017)

    2017

  13. [21]

    H.-Y. Yang, A. M. L¨ auchli, F. Mila, and K. P. Schmidt, Phys. Rev. Lett. 105, 267204 (2010)

    2010

  14. [22]

    Morita, S

    H. Morita, S. Watanabe, and M. Imada, Journal of the Physical Society of Japan 71, 2109 (2002)

    2002

  15. [23]

    Kyung and A.-M

    B. Kyung and A.-M. S. Tremblay, Phys. Rev. Lett. 97, 046402 (2006)

    2006

  16. [24]

    Ohashi, T

    T. Ohashi, T. Momoi, H. Tsunetsugu, and N. Kawakami, Phys. Rev. Lett. 100, 076402 (2008)

    2008

  17. [25]

    Liebsch, H

    A. Liebsch, H. Ishida, and J. Merino, Phys. Rev. B 79, 195108 (2009)

    2009

  18. [26]

    Galanakis, T

    D. Galanakis, T. D. Stanescu, and P. Phillips, Phys. Rev. B 79, 115116 (2009)

    2009

  19. [27]

    T. Sato, K. Hattori, and H. Tsunetsugu, Phys. Rev. B 86, 235137 (2012)

    2012

  20. [28]

    H. Lee, G. Li, and H. Monien, Phys. Rev. B 78, 205117 (2008)

    2008

  21. [29]

    H. T. Dang, X. Y. Xu, K.-S. Chen, Z. Y. Meng, and S. Wessel, Phys. Rev. B 91, 155101 (2015)

    2015

  22. [30]

    Q. Q. Ge, H. C. Xu, X. P. Shen, M. Xia, B. P. Xie, F. Chen, Y. Zhang, R. Kato, T. Tsumuraya, T. Miyazaki, M. Matsunami, S. Kimura, and D. L. Feng, Phys. Rev. B 89, 075105 (2014)

    2014

  23. [31]

    Lemmens, K

    P. Lemmens, K. Y. Choi, V. Gnezdilov, E. Y. Sherman, D. P. Chen, C. T. Lin, F. C. Chou, and B. Keimer, Phys. Rev. Lett. 96, 167204 (2006)

    2006

  24. [32]

    Shimizu, T

    Y. Shimizu, T. Hiramatsu, M. Maesato, A. Otsuka, H. Yamochi, A. Ono, M. Itoh, M. Yoshida, M. Takigawa, Y. Yoshida, and G. Saito, Phys. Rev. Lett. 117, 107203 (2016)

    2016

  25. [33]

    S. Ito, N. Kurita, H. Tanaka, S. Ohira-Kawamura, K. Nakajima, S. Itoh, K. Kuwahara, and K. Kakurai, Nature Communications 8, 235 (2017)

    2017

  26. [34]

    V. I. Iglovikov, E. Khatami, and R. T. Scalettar, Phys. Rev. B 92, 045110 (2015)

    2015

  27. [35]

    A. N. Rubtsov, M. I. Katsnelson, and A. I. Lichtenstein, Phys. Rev. B 77, 033101 (2008)

    2008

  28. [36]

    Brener, H

    S. Brener, H. Hafermann, A. N. Rubtsov, M. I. Katsnel- son, and A. I. Lichtenstein, Phys. Rev. B 77, 195105 (2008)

    2008

  29. [37]

    G. Li, H. Lee, and H. Monien, Phys. Rev. B 78, 195105 (2008)

    2008

  30. [38]

    Strong electronic correlations: Dynamical mean-field theory and beyond,

    H. Hafermann, F. Lechermann, A. N. Rubtsov, M. I. Katsnelson, A. Georges, and A. I. Lichtenstein, “Strong electronic correlations: Dynamical mean-field theory and beyond,” in Modern Theories of Many-Particle Systems in Condensed Matter Physics , edited by D. C. Cabra, A. Honeck...

    2012

  31. [39]

    A. E. Antipov, E. Gull, and S. Kirchner, Phys. Rev. Lett. 112, 226401 (2014)

    2014

  32. [40]

    Rohringer, H

    G. Rohringer, H. Hafermann, A. Toschi, A. A. Katanin, A. E. Antipov, M. I. Katsnelson, A. I. Lichtenstein, A. N. Rubtsov, and K. Held, Rev. Mod. Phys. 90, 025003 (2018)

    2018

  33. [41]

    A. E. Antipov, J. P. LeBlanc, and E. Gull, Physics Pro- cedia 68, 43 (2015), proceedings of the 28th Workshop on Computer Simulation Studies in Condensed Matter Physics (CSP2015). 6

    2015

  34. [42]

    Georges, G

    A. Georges, G. Kotliar, W. Krauth, and M. J. Rozen- berg, Rev. Mod. Phys. 68, 13 (1996)

    1996

  35. [43]

    E. Gull, A. J. Millis, A. I. Lichtenstein, A. N. Rubtsov, M. Troyer, and P. Werner, Rev. Mod. Phys. 83, 349 (2011)

    2011

  36. [44]

    E. Gull, P. Werner, O. Parcollet, and M. Troyer, EPL 82, 57003 (2008)

    2008

  37. [45]

    E. Gull, P. Staar, S. Fuchs, P. Nukala, M. S. Summers, T. Pruschke, T. C. Schulthess, and T. Maier, Phys. Rev. B 83, 075122 (2011)

    2011

  38. [46]

    J. P. F. LeBlanc, A. E. Antipov, F. Becca, I. W. Bulik, G. K.-L. Chan, C.-M. Chung, Y. Deng, M. Ferrero, T. M. Henderson, C. A. Jim´ enez-Hoyos, E. Kozik, X.-W. Liu, A. J. Millis, N. V. Prokof’ev, M. Qin, G. E. Scuseria, H. Shi, B. V. Svistunov, L. F. Tocchio, I. S. Tupitsyn, ...

    2015

  39. [47]

    Ribic, P

    T. Ribic, P. Gunacker, S. Iskakov, M. Wallerberger, G. Rohringer, A. N. Rubtsov, E. Gull, and K. Held, Phys. Rev. B 96, 235127 (2017)

    2017

  40. [48]

    Iskakov, A

    S. Iskakov, A. E. Antipov, and E. Gull, Phys. Rev. B 94, 035102 (2016)

    2016

  41. [49]

    J. P. F. LeBlanc, S. Li, X. Chen, R. Levy, A. E. Antipov, A. J. Millis, and E. Gull, Phys. Rev. B 100, 075123 (2019)

    2019

  42. [50]

    R. Levy, J. LeBlanc, and E. Gull, Computer Physics Communications 215, 149 (2017)

    2017

  43. [51]

    Gaenko, A

    A. Gaenko, A. Antipov, G. Carcassi, T. Chen, X. Chen, Q. Dong, L. Gamper, J. Gukelberger, R. Igarashi, S. Iskakov, M. Knz, J. LeBlanc, R. Levy, P. Ma, J. Paki, H. Shinaoka, S. Todo, M. Troyer, and E. Gull, Computer Physics Communications 213, 235 (2017)

    2017

  44. [52]

    Jarrell and J

    M. Jarrell and J. Gubernatis, Physics Reports 269, 133 (1996)

    1996

  45. [53]

    G. Li, A. E. Antipov, A. N. Rubtsov, S. Kirchner, and W. Hanke, Phys. Rev. B 89, 161118(R) (2014)

    2014

  46. [54]

    Laubach, R

    M. Laubach, R. Thomale, C. Platt, W. Hanke, and G. Li, Phys. Rev. B 91, 245125 (2015)

    2015

  47. [55]

    The white dashed line rep- resents the boundary of the Brillouin zone

    for these three values of U are plotted in panels (a), (b), and (c), respectively. The white dashed line rep- resents the boundary of the Brillouin zone. Static spin correlations are enhanced as U increases. At U = 12t, the static spin correlations show a clear peak at the K p...

  48. [56]

    See Supplementary Material at [URL will be inserted by publisher] for the details

  49. [57]

    Yoshioka, A

    T. Yoshioka, A. Koga, and N. Kawakami, Phys. Rev. Lett. 103, 036401 (2009)

    2009

  50. [58]

    Hafermann, E

    H. Hafermann, E. G. C. P. van Loon, M. I. Katsnelson, A. I. Lichtenstein, and O. Parcollet, Phys. Rev. B 90, 235105 (2014)

    2014

  51. [59]

    Nakamura, Y

    K. Nakamura, Y. Yoshimoto, T. Kosugi, R. Arita, and M. Imada, Journal of the Physical Society of Japan 78, 083710 (2009)

    2009

  52. [60]

    X. Chen, J. P. F. LeBlanc, and E. Gull, Nature Com- munications 8, 14986 (2017)

    2017

  53. [61]

    Magnetic and charge susceptibilities in the half-filled triangular lattice Hubbard model

    R. T. Clay, N. Gomes, and S. Mazumdar, arXiv , 1904.03067 (2019). 7 Supplementary material for “Magnetic and charge susceptibilities in the half-filled triangular lattice Hubbard model” Shaozhi Li1 and Emanuel Gull 1,2 1Department of Physics, University of Michigan, Ann Arbor, ...

    2019 arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.