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arxiv: 2607.02326 · v1 · pith:KI7J43HRnew · submitted 2026-07-02 · ❄️ cond-mat.str-el

Fundamental limitations of single-particle Green's-function zeroes as probes of many-body topology

Emile Pangburn , Olivier Gingras This is my paper

Pith reviewed 2026-07-03 05:41 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords Green's functionstopological invariantsmany-body topologyinteracting systemsSSH modelFock sectorsquasiparticlesspin-spin interaction
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0 comments X

The pith

Topological invariants from single-particle Green's functions cannot reliably diagnose the topology of interacting many-body states.

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

The paper establishes that single-particle Green's function topological invariants fail to capture the actual topology of many-body states once interactions are present. It demonstrates this with coupled interacting SSH chains, where a spin-spin interaction renders the many-body ground state topologically trivial yet leaves the GF-based invariant unchanged. The failure occurs because the Green's function cannot access the electronic excitations within the Fock sectors that sustain the topological degeneracy. Consequently the zeroes of the Green's function do not mark physical topological quasiparticles. A sympathetic reader would care because this limitation undermines a widely used diagnostic tool for classifying interacting topological phases.

Core claim

We show that topological invariants constructed from single-particle Green's functions (GFs) cannot reliably diagnose the topology of interacting many-body states. Using coupled interacting SSH chains as a minimal example, we demonstrate that a spin-spin interaction can trivialize the many-body ground state without affecting the GF topological invariant. This breakdown originates from the GF's inability to probe electronic excitations in the Fock sectors responsible for the topological degeneracy. Consequently, GF zeroes are not associated with physical topological quasiparticles and cannot generally characterize interacting topological phases.

What carries the argument

The single-particle Green's function topological invariant, which fails to track many-body topology because it cannot probe excitations in the Fock sectors that protect the topological degeneracy.

If this is right

  • GF zeroes do not correspond to physical topological quasiparticles in interacting systems.
  • Single-particle GF invariants cannot generally classify interacting topological phases.
  • Topology in interacting systems must be diagnosed with probes that access the relevant Fock sectors.
  • The breakdown applies whenever topological degeneracy is carried by excitations invisible to the single-particle GF.

Where Pith is reading between the lines

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

  • Similar limitations may affect other single-particle spectral functions used to infer topology in the presence of interactions.
  • Many-body extensions of the Green's function or correlation functions involving multiple particles could be required for reliable diagnosis.
  • Results obtained from GF-based invariants in strongly interacting materials should be reexamined for consistency with the actual many-body ground state.

Load-bearing premise

The coupled interacting SSH chains provide a valid minimal example in which a spin-spin interaction changes the many-body ground-state topology while leaving the single-particle GF invariant unchanged.

What would settle it

An explicit calculation or measurement in the coupled interacting SSH chains showing that the GF topological invariant changes precisely when the spin-spin interaction trivializes the many-body ground state.

Figures

Figures reproduced from arXiv: 2607.02326 by Emile Pangburn, Olivier Gingras.

Figure 1
Figure 1. Figure 1: FIG. 1. Trivialization of two topological chains. Left figures: [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Inaccurate topology inferred from Green’s function zeroes [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
read the original abstract

We show that topological invariants constructed from single-particle Green's functions (GFs) cannot reliably diagnose the topology of interacting many-body states. Using coupled interacting SSH chains as a minimal example, we demonstrate that a spin-spin interaction can trivialize the many-body ground state without affecting the GF topological invariant. This breakdown originates from the GF's inability to probe electronic excitations in the Fock sectors responsible for the topological degeneracy. Consequently, GF zeroes are not associated with physical topological quasiparticles and cannot generally characterize interacting topological phases.

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

0 major / 2 minor

Summary. The manuscript claims that topological invariants constructed from single-particle Green's functions (GFs) cannot reliably diagnose the topology of interacting many-body states. Using coupled interacting SSH chains as a minimal example, it shows that a spin-spin interaction can trivialize the many-body ground state without affecting the GF topological invariant, because the GF cannot probe excitations in the Fock sectors responsible for topological degeneracy. The paper concludes that GF zeroes are not associated with physical topological quasiparticles and cannot generally characterize interacting topological phases.

Significance. If the counterexample holds, the result is significant for condensed-matter theory of interacting topological phases, as it identifies a concrete mechanism by which single-particle GF methods miss many-body topological features tied to Fock-space structure. The paper's strength is its use of a minimal, falsifiable model example rather than a general derivation, making the limitation explicit and testable.

minor comments (2)
  1. The abstract and introduction would benefit from a brief statement of the explicit form of the GF topological invariant employed (e.g., winding number or Zak phase constructed from the GF), to allow immediate comparison with prior literature on GF-based invariants.
  2. Figure captions should explicitly label the non-interacting versus interacting cases and state the parameter values used for the spin-spin coupling strength.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and for recommending acceptance. The report accurately summarizes the central claim and its implications for the use of single-particle Green's functions in diagnosing interacting topological phases.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central claim is established via an explicit counterexample (coupled interacting SSH chains with spin-spin interaction) rather than any derivation, ansatz, or fitted parameter that reduces to its own inputs. The abstract and described mechanism directly exhibit the GF invariant remaining unchanged while the many-body topology is trivialized, with the explanation tied to Fock-sector access limitations; this is an independent, falsifiable construction with no self-definitional steps, no load-bearing self-citations, and no renaming of known results. The argument is self-contained against the model's explicit construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper relies on the standard construction of topological invariants from the single-particle Green's function, which is taken from prior literature; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Single-particle Green's functions can be used to construct topological invariants that diagnose many-body states
    This is the premise the paper tests and finds insufficient for interacting cases.

pith-pipeline@v0.9.1-grok · 5604 in / 1100 out tokens · 24715 ms · 2026-07-03T05:41:05.202784+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

93 extracted references · 93 canonical work pages · 1 internal anchor

  1. [1]

    In con- trast, a finiteJ 12 introduces a purely many-body interaction that preserves all symmetries

    A finitet 12 couples the chains at the single- particle level which breaks the sublattice symmetry. In con- trast, a finiteJ 12 introduces a purely many-body interaction that preserves all symmetries. Trivialization through coupling.—In order to demonstrate that GF zeroes do not reliably characterize the topology of the many-body state in the bulk, in par...

    work page

  2. [2]

    On the other hand, in Fig

    We find that any finiteJ 12 or t12 opens a spin gap, reflecting the formation of singlets be- tween the two topological edge spin-½ modes and therefore signaling the trivialization of the system as soon as inter-chain coupling is introduced. On the other hand, in Fig. 2(b), we present the GF topolog- ical indicatorZ[G]for three cases: in full blue, dotted...

    work page

  3. [3]

    Alexandradinata, X

    A. Alexandradinata, X. Dai, and B. A. Bernevig, Wilson-loop characterization of inversion-symmetric topological insulators, Phys. Rev. B89, 155114 (2014)

    work page 2014

  4. [4]

    C.-K. Chiu, J. C. Y . Teo, A. P. Schnyder, and S. Ryu, Classifica- tion of topological quantum matter with symmetries, Rev. Mod. Phys.88, 035005 (2016)

    work page 2016

  5. [5]

    Chen, Z.-C

    X. Chen, Z.-C. Gu, and X.-G. Wen, Classification of gapped symmetric phases in one-dimensional spin systems, Phys. Rev. B83, 035107 (2011)

    work page 2011

  6. [6]

    Pollmann, E

    F. Pollmann, E. Berg, A. M. Turner, and M. Oshikawa, Symme- try protection of topological phases in one-dimensional quan- tum spin systems, Phys. Rev. B85, 075125 (2012)

    work page 2012

  7. [7]

    Senthil, Symmetry-Protected Topological Phases of Quan- tum Matter, Annual Review of Condensed Matter Physics6, 299 (2015)

    T. Senthil, Symmetry-Protected Topological Phases of Quan- tum Matter, Annual Review of Condensed Matter Physics6, 299 (2015)

    work page 2015

  8. [8]

    Verresen, R

    R. Verresen, R. Moessner, and F. Pollmann, One-dimensional symmetry protected topological phases and their transitions, Phys. Rev. B96, 165124 (2017)

    work page 2017

  9. [9]

    Wang, X.-L

    Z. Wang, X.-L. Qi, and S.-C. Zhang, Topological Order Pa- rameters for Interacting Topological Insulators, Phys. Rev. Lett. 105, 256803 (2010)

    work page 2010

  10. [10]

    Wang and S.-C

    Z. Wang and S.-C. Zhang, Simplified Topological Invariants for Interacting Insulators, Phys. Rev. X2, 031008 (2012)

    work page 2012

  11. [11]

    Gurarie, Single-particle green’s functions and interacting topological insulators, Phys

    V . Gurarie, Single-particle green’s functions and interacting topological insulators, Phys. Rev. B83, 085426 (2011)

    work page 2011

  12. [12]

    S. R. Manmana, A. M. Essin, R. M. Noack, and V . Gu- rarie, Topological invariants and interacting one-dimensional fermionic systems, Phys. Rev. B86, 205119 (2012)

    work page 2012

  13. [13]

    Yoshida, R

    T. Yoshida, R. Peters, S. Fujimoto, and N. Kawakami, Charac- terization of a Topological Mott insulator in One Dimension, Phys. Rev. Lett.112, 196404 (2014)

    work page 2014

  14. [14]

    Iraola, N

    M. Iraola, N. Heinsdorf, A. Tiwari, D. Lessnich, T. Mertz, F. Ferrari, M. H. Fischer, S. M. Winter, F. Pollmann, T. Neupert, R. Valent´ı, and M. G. Vergniory, Towards a topological quan- tum chemistry description of correlated systems: The case of the Hubbard diamond chain, Phys. Rev. B104, 195125 (2021)

    work page 2021

  15. [15]

    Lessnich, S

    D. Lessnich, S. M. Winter, M. Iraola, M. G. Vergniory, and R. Valent´ı, Elementary band representations for the single- particle Green’s function of interacting topological insulators, Phys. Rev. B104, 085116 (2021)

    work page 2021

  16. [16]

    Blason and M

    A. Blason and M. Fabrizio, Unified role of Green’s function poles and zeros in correlated topological insulators, Phys. Rev. B108, 125115 (2023)

    work page 2023

  17. [17]

    Bollmann, C

    S. Bollmann, C. Setty, U. F. P. Seifert, and E. J. K ¨onig, Topo- logical Green’s Function Zeros in an Exactly Solved Model and Beyond, Phys. Rev. Lett.133, 136504 (2024)

    work page 2024

  18. [18]

    Peralta Gavensky, S

    L. Peralta Gavensky, S. Sachdev, and N. Goldman, Connect- ing the many-body chern number to luttinger’s theorem through stˇreda’s formula, Phys. Rev. Lett.131, 236601 (2023)

    work page 2023

  19. [19]

    Wagner, L

    N. Wagner, L. Crippa, A. Amaricci, P. Hansmann, M. Klett, E. J. K ¨onig, T. Sch ¨afer, D. D. Sante, J. Cano, A. J. Millis, A. Georges, and G. Sangiovanni, Mott insulators with bound- ary zeros, Nature Communications14, 7531 (2023)

    work page 2023

  20. [20]

    Wagner, D

    N. Wagner, D. Guerci, A. J. Millis, and G. Sangiovanni, Edge Zeros and Boundary Spinons in Topological Mott Insulators, Phys. Rev. Lett.133, 126504 (2024)

    work page 2024

  21. [21]

    Setty, F

    C. Setty, F. Xie, S. Sur, L. Chen, M. G. Vergniory, and Q. Si, Electronic properties, correlated topology, and Green’s function zeros, Phys. Rev. Res.6, 033235 (2024)

    work page 2024

  22. [22]

    Setty, S

    C. Setty, S. Sur, L. Chen, F. Xie, H. Hu, S. Paschen, J. Cano, and Q. Si, Symmetry constraints and spectral crossing in a Mott in- sulator with Green’s function zeros, Phys. Rev. Res.6, L032018 (2024)

    work page 2024

  23. [23]

    Nourafkan and G

    R. Nourafkan and G. Kotliar, Electric polarization in correlated insulators, Phys. Rev. B88, 155121 (2013)

    work page 2013

  24. [24]

    T. N. Dionne, S. Villodre, M. Iraola, and M. G. Vergniory, Char- acterizing Mott Insulators in the Interacting One-Body Picture (2026), arXiv:2511.07331 [cond-mat.str-el]

    work page arXiv 2026

  25. [25]

    E. J. K ¨onig and A. Mitra, Topological Floquet Green’s function zeros (2026), arXiv:2602.21199 [cond-mat.mes-hall]

    work page arXiv 2026

  26. [26]

    Poles-zeros duality in semi-holographic Mott insulators

    T. K ¨ogel, A. Caddeo, A. Pitters, F. Paoletti, L. Crippa, G. Sangiovanni, R. Meyer, and J. Erdmenger, Poles-zeros duality in semi-holographic mott insulators, arXiv preprint arXiv:2605.20321 (2026)

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  27. [27]

    Mitra, F

    S. Mitra, F. Xie, M. Kolmer, Q. Si, and C. Setty, Signatures of green’s function zeros and their topology using impurity spec- troscopy, arXiv preprint arXiv:2602.23477 (2026)

    work page arXiv 2026

  28. [28]

    Dzyaloshinskii, Some consequences of the Luttinger theo- rem: The luttinger surfaces in non-fermi liquids and mott insu- lators, Phys

    I. Dzyaloshinskii, Some consequences of the Luttinger theo- rem: The luttinger surfaces in non-fermi liquids and mott insu- lators, Phys. Rev. B68, 085113 (2003)

    work page 2003

  29. [29]

    T. D. Stanescu, P. Phillips, and T.-P. Choy, Theory of the Luttinger surface in doped Mott insulators, Phys. Rev. B75, 104503 (2007)

    work page 2007

  30. [30]

    Rosch, Breakdown of Luttinger’s theorem in two-orbital Mott insulators, The European Physical Journal B59, 495 (2007)

    A. Rosch, Breakdown of Luttinger’s theorem in two-orbital Mott insulators, The European Physical Journal B59, 495 (2007)

    work page 2007

  31. [31]

    Seki and S

    K. Seki and S. Yunoki, Topological interpretation of the Lut- tinger theorem, Phys. Rev. B96, 085124 (2017)

    work page 2017

  32. [32]

    Skolimowski and M

    J. Skolimowski and M. Fabrizio, Luttinger’s theorem in the presence of Luttinger surfaces, Phys. Rev. B106, 045109 (2022)

    work page 2022

  33. [33]

    K. B. Dave, P. W. Phillips, and C. L. Kane, Absence of Lut- tinger’s Theorem due to Zeros in the Single-Particle Green Function, Phys. Rev. Lett.110, 090403 (2013)

    work page 2013

  34. [34]

    T. D. Stanescu and G. Kotliar, Fermi arcs and hidden zeros of the Green function in the pseudogap state, Phys. Rev. B74, 125110 (2006)

    work page 2006

  35. [35]

    Sakai, Y

    S. Sakai, Y . Motome, and M. Imada, Evolution of Electronic Structure of Doped Mott Insulators: Reconstruction of Poles and Zeros of Green’s Function, Phys. Rev. Lett.102, 056404 (2009)

    work page 2009

  36. [36]

    Sakai, Y

    S. Sakai, Y . Motome, and M. Imada, Doped high-T c cuprate superconductors elucidated in the light of zeros and poles of the electronic Green’s function, Phys. Rev. B82, 134505 (2010)

    work page 2010

  37. [37]

    K.-Y . Yang, T. M. Rice, and F.-C. Zhang, Phenomenological theory of the pseudogap state, Phys. Rev. B73, 174501 (2006)

    work page 2006

  38. [38]

    M. S. Scheurer, S. Chatterjee, W. Wu, M. Ferrero, A. Georges, and S. Sachdev, Topological order in the pseudogap metal, Pro- ceedings of the National Academy of Sciences115, E3665 (2018)

    work page 2018

  39. [39]

    P. Worm, M. Reitner, K. Held, and A. Toschi, Fermi and Lut- tinger Arcs: Two Concepts, Realized on One Surface, Phys. Rev. Lett.133, 166501 (2024)

    work page 2024

  40. [40]

    Fabrizio, Emergent quasiparticles at Luttinger surfaces, Na- ture Communications13, 1561 (2022)

    M. Fabrizio, Emergent quasiparticles at Luttinger surfaces, Na- ture Communications13, 1561 (2022)

    work page 2022

  41. [41]

    Fabrizio, Spin-Liquid Insulators Can Be Landau’s Fermi Liquids, Phys

    M. Fabrizio, Spin-Liquid Insulators Can Be Landau’s Fermi Liquids, Phys. Rev. Lett.130, 156702 (2023)

    work page 2023

  42. [42]

    Blason, I

    A. Blason, I. Pasqua, M. Ferrero, and M. Fabrizio, Luttinger surface dominance and Fermi liquid behavior of topological Kondo insulatorsSmB 6 andYbB 12, Phys. Rev. B110, 235115 (2024)

    work page 2024

  43. [43]

    Pasqua and M

    I. Pasqua and M. Fabrizio, Fermi-liquid corrections to the in- trinsic anomalous Hall conductivity of topological metals, Sci- 6 Post Phys.19, 014 (2025)

    work page 2025

  44. [44]

    He, H.-Q

    Y .-Y . He, H.-Q. Wu, Z. Y . Meng, and Z.-Y . Lu, Topological invariants for interacting topological insulators. I. Efficient nu- merical evaluation scheme and implementations, Phys. Rev. B 93, 195163 (2016)

    work page 2016

  45. [45]

    He, H.-Q

    Y .-Y . He, H.-Q. Wu, Z. Y . Meng, and Z.-Y . Lu, Topological invariants for interacting topological insulators. II. Breakdown of single-particle Green’s function formalism, Phys. Rev. B93, 195164 (2016)

    work page 2016

  46. [46]

    J. Zhao, P. Mai, B. Bradlyn, and P. Phillips, Failure of Topolog- ical Invariants in Strongly Correlated Matter, Phys. Rev. Lett. 131, 106601 (2023)

    work page 2023

  47. [47]

    A. A. Aligia, A. M. Lobos, L. P. Gavensky, and C. J. Gazza, Probing Boundary Spins in the Su-Schrieffer-Heeger-Hubbard model (2025), arXiv:2511.17173 [cond-mat.str-el]

    work page arXiv 2025

  48. [48]

    A. A. Markov, A. M. Nikishin, N. R. Cooper, N. Goldman, and L. P. Gavensky, Luttinger’s Theorem Violation and Green’s Function Topological Invariants in a Fractional Chern Insulator (2026), arXiv:2603.17006 [cond-mat.str-el]

    work page arXiv 2026

  49. [49]

    W. P. Su, J. R. Schrieffer, and A. J. Heeger, Solitons in Poly- acetylene, Phys. Rev. Lett.42, 1698 (1979)

    work page 1979

  50. [50]

    Fidkowski and A

    L. Fidkowski and A. Kitaev, Effects of interactions on the topo- logical classification of free fermion systems, Phys. Rev. B81, 134509 (2010)

    work page 2010

  51. [51]

    Queiroz, E

    R. Queiroz, E. Khalaf, and A. Stern, Dimensional Hierarchy of Fermionic Interacting Topological Phases, Phys. Rev. Lett.117, 206405 (2016)

    work page 2016

  52. [52]

    Pangburn, C

    E. Pangburn, C. P ´epin, and A. Banerjee, Topological charge ex- citations and Green’s function zeros in paramagnetic Mott in- sulators, Phys. Rev. B112, 085105 (2025)

    work page 2025

  53. [53]

    Weinberg, Evidence That the Deuteron Is Not an Elementary Particle, Phys

    S. Weinberg, Evidence That the Deuteron Is Not an Elementary Particle, Phys. Rev.137, B672 (1965)

    work page 1965

  54. [54]

    W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, Quantized electric multipole insulators, Science357, 61 (2017)

    work page 2017

  55. [56]

    Chen and P

    K.-T. Chen and P. A. Lee, Unified formalism for calculating polarization, magnetization, and more in a periodic insulator, Phys. Rev. B84, 205137 (2011)

    work page 2011

  56. [57]

    D. V . Else and R. Thorngren, Topological theory of Lieb- Schultz-Mattis theorems in quantum spin systems, Phys. Rev. B101, 224437 (2020)

    work page 2020

  57. [58]

    Fuchs and F

    J.-N. Fuchs and F. Pi ´echon, Orbital embedding and topology of one-dimensional two-band insulators, Phys. Rev. B104, 235428 (2021)

    work page 2021

  58. [59]

    Guzm ´an, D

    M. Guzm ´an, D. Bartolo, and D. Carpentier, Geometry and topology tango in ordered and amorphous chiral matter, SciPost Phys.12, 038 (2022)

    work page 2022

  59. [60]

    Lehmann, L

    C. Lehmann, L. Crippa, G. Sangiovanni, and J. C. Budich, Probing Green’s Function Zeros by Cotunneling through Mott Insulators, Phys. Rev. Lett.135, 106303 (2025)

    work page 2025

  60. [61]

    E. R. Gagliano and C. A. Balseiro, Dynamic correlation func- tions in quantum many-body systems at zero temperature, Phys. Rev. B38, 11766 (1988)

    work page 1988

  61. [62]

    Dagotto, Correlated electrons in high-temperature supercon- ductors, Rev

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

    work page 1994

  62. [63]

    S. R. White, Density matrix formulation for quantum renormal- ization groups, Phys. Rev. Lett.69, 2863 (1992)

    work page 1992

  63. [64]

    Schollw ¨ock, The density-matrix renormalization group, Rev

    U. Schollw ¨ock, The density-matrix renormalization group, Rev. Mod. Phys.77, 259 (2005)

    work page 2005

  64. [65]

    Schollw ¨ock, The density-matrix renormalization group in the age of matrix product states, Annals of Physics326, 96 (2011)

    U. Schollw ¨ock, The density-matrix renormalization group in the age of matrix product states, Annals of Physics326, 96 (2011)

    work page 2011

  65. [66]

    Fishman, S

    M. Fishman, S. R. White, and E. M. Stoudenmire, The ITen- sor Software Library for Tensor Network Calculations, SciPost Phys. Codebases , 4 (2022)

    work page 2022

  66. [67]

    Zhang, J

    S. Zhang, J. Carlson, and J. E. Gubernatis, Constrained path Monte Carlo method for fermion ground states, Phys. Rev. B 55, 7464 (1997)

    work page 1997

  67. [68]

    Zhang and H

    S. Zhang and H. Krakauer, Quantum Monte Carlo Method us- ing Phase-Free Random Walks with Slater Determinants, Phys. Rev. Lett.90, 136401 (2003)

    work page 2003

  68. [69]

    Eskridgeet al., private communication; SAFIRE (2026), https://safire.flatironinstitute.org/

    B. Eskridgeet al., private communication; SAFIRE (2026), https://safire.flatironinstitute.org/

    work page 2026

  69. [70]

    Hubbard, Electron correlations in narrow energy bands, Pro- ceedings of the Royal Society of London

    J. Hubbard, Electron correlations in narrow energy bands, Pro- ceedings of the Royal Society of London. A. Mathematical and Physical Sciences276, 238 (1963)

    work page 1963

  70. [71]

    Hubbard, Electron correlations in narrow energy bands III

    J. Hubbard, Electron correlations in narrow energy bands III. An improved solution, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences281, 401 (1964)

    work page 1964

  71. [72]

    L. M. Roth, Electron Correlation in Narrow Energy Bands. I. The Two-Pole Approximation in a NarrowSBand, Phys. Rev. 184, 451 (1969)

    work page 1969

  72. [73]

    Mancini and A

    F. Mancini and A. Avella, The Hubbard model within the equa- tions of motion approach, Advances in Physics53, 537 (2004)

    work page 2004

  73. [74]

    Haurie, M

    L. Haurie, M. Grandadam, E. Pangburn, A. Banerjee, S. Burdin, and C. P ´epin, Bands renormalization and superconductivity in the strongly correlated Hubbard model using composite opera- tors method, Journal of Physics: Condensed Matter36, 255601 (2024)

    work page 2024

  74. [75]

    Banerjee, E

    A. Banerjee, E. Pangburn, C. Mahato, A. Ghosal, and C. P´epin, Charge density wave solutions of the Hubbard model in the composite operator formalism, Phys. Rev. B111, 165123 (2025)

    work page 2025

  75. [76]

    M. V . Berry, Quantal phase factors accompanying adiabatic changes, Proceedings of the Royal Society of London. A. Math- ematical and Physical Sciences392, 45 (1984)

    work page 1984

  76. [77]

    Xiao, M.-C

    D. Xiao, M.-C. Chang, and Q. Niu, Berry phase effects on elec- tronic properties, Rev. Mod. Phys.82, 1959 (2010). 1 Supplemental Materials to Fundamental limitations of single-particle Green’s-function zeroes as probes of many-body topology Emile Pangburn1,2, Olivier Gingras 2,1 1Institut de Physique Th´eorique, Universit´e Paris Saclay, CEA CNRS, Orme de...

    work page 1959

  77. [78]

    Lehmann representation of the Green’s function We study the relationship between the topologies of the ground state and of the GF in fermionic models. In particular, we focus on single-particle retarded (R) GF defined as GR ij(t) =−iθ(t) Dn c† j(t), ci oE ,(A1) wherec i (c† i ) is the annihilation (creation) operator of an elec- tron with quantum numbersi...

    work page

  78. [79]

    Our discussion follows Ref

    Existence of Green’s function zeroes We now discuss the relationship between the number of poles and zeroes of the single-particle GF within a fixed set of quantum numbers. Our discussion follows Ref. S29. For diagonal GF elements associated with conserved quan- tum numbers, the difference between the number of poles and zeroes is invariant under continuo...

    work page

  79. [80]

    A zero occurs at a frequency ωwhen this determinant vanishes, indicating that the GF pos- sesses a zero mode at that energy

    Determinant of the Green’s function In practice, GF zeroes are identified by examining the deter- minant of the single-particle GF. A zero occurs at a frequency ωwhen this determinant vanishes, indicating that the GF pos- sesses a zero mode at that energy. Sayw z is a zero, then |detG(ω z)|= 0.(A4) GF zeroes can also be understood as divergences of the se...

    work page

  80. [81]

    Chiral symmetry and topological invariants The topology of the SSH chain is protected by sublattice- symmetry, allowing the definition of topological invariants. This symmetry acts on the many-body HamiltonianHas ˆSH ˆS −1 =H,where ˆS −1ciσ ˆS= (−1) ic† iσ.(A6) This transformation assigns opposite signs to the two sublat- tices, reflecting the bipartite s...

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