Pith. sign in

REVIEW 3 major objections 6 minor 98 references

Topological charge excitations and Green's function zeros in paramagnetic Mott insulators

T0 review · 3 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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

Pith's one-line read Interactions can make a Mott insulator's occupied charge-excitation bands carry a nonzero Chern number, and can make its Green's-function zeros carry their own nonzero winding number in a different parameter regime.

desk verdict A genuinely new COM phase diagram for the two-band Chern-Hubbard model, with a credible pole-side TMBI result and a shakier zero-side TMZ result; worth a serious referee, but not a quick accept. read the letter →

arxiv 2412.13302 v4 pith:FJKKQF55 submitted 2024-12-17 cond-mat.str-el

Emile Pangburn , Catherine Pépin , Anurag Banerjee This is my paper · ORCID
classification cond-mat.str-el
keywords MottinsulatorGreen'sfunctionzeroscompositeoperatormethodChern-Hubbardmodeltopologicalbandholon-doublonexcitationswindingnumberbulk-boundarycorrespondence
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 studies the two-band Chern-Hubbard model at half-filling with strong on-site repulsion and argues that the Mott insulating state can be topological in two separate ways. Treating electrons as holon and doublon excitations inside the composite operator method, the authors find a parameter regime where the occupied single-particle Hubbard bands carry a nonzero winding number, producing a topological Mott band insulator with a gapless charged edge and quantized Hall conductivity. In a different regime, the bands of Green's function zeros acquire their own nonzero winding number, forming a topological Mott zero phase whose edge carries a gapless but charge-neutral zero mode and whose Hall conductivity is zero. The paper's phase diagram maps both windings as functions of crystal-field splitting and interaction strength, and junction calculations show that pole edge modes and zero edge modes coexist without annihilating. The broader interest is that topology of Mott insulators can be carried not only by quasiparticles but by where the Green's function vanishes.

What carries the argument

The machinery is the composite operator method (COM) in its two-pole approximation. The electron operator is written c = ξ + η with holon ξiασ = ciασ(1−niασ) and doublon ηiασ = ciασ niασ; the Green's function is built from the 4-component local basis Ψi = (ξs,ηs,ξp,ηp), and the equation of motion is truncated by assuming the current [H,Ψ] stays proportional to Ψ, so G(ω) = ((ω−E)1)^{-1} I with E = M $I^{{-1}}$ and M, I computed from self-consistently Roth-decoupled correlators. From this the electronic Green's function and its zeros are obtained. The topological invariant is the winding number N3[G] of the interacting Green's function, which for non-interacting systems equals the Chern number; for bands of poles and bands of zeros the paper computes N3 in the occupied subspaces defined by a chosen chemical potential. For the zeros, an effective Hamiltonian H0(k) = Tr_{ξη}[E(k)ρ0(k)] built from an equal coherent superposition of holons and doublons reproduces the zero dispersion and its eigenvectors, letting the winding of the zero bands be computed as ordinary band topology. Bulk-boundary correspondence is checked in real space with open boundaries, π-flux defects, and TMBI–TMZ junctions.

What would settle it

A numerically exact calculation of the same two-band Chern-Hubbard model at half-filling on a cylinder, for parameters such as Us=12.2t and M=4.36t, should show a gapless charged edge mode and quantized Hall conductance if the TMBI claim is right, or no such mode if it is wrong. For the TMZ parameters, such as Us=13.71t and M=0.53t, an exact calculation should find the Green's-function-zero gap closing at the boundary while the single-particle excitation gap stays open; if the zeros gap remains open, the TMZ claim fails.

Watch

Extended reading notes

Core claim

The central discovery is that on-site repulsion alone, combined with crystal-field-induced band inversion, can make the charge excitations of a Mott insulator topological. In the composite operator description the electron splits into a holon (an empty site) and a doublon (a doubly occupied site); the occupied lower Hubbard bands are holon-dominated, and when the crystal field M becomes large enough, a holon band of one orbital hybridizes with the doublon band of the other, exchanging inversion eigenvalues and giving the occupied bands a nonzero Chern number N3,σ. The authors call this the topological Mott band insulator (TMBI), and show it has a gapless edge state carrying charge and a Hall conductivity σxy = C $e^{2}$/h computed from the Streda formula. Independently, the interacting Green's function G can have bands of zeros inside the Mott gap; these zeros are interpreted as tightly bound holon-doublon pairs and are described by an effective local Hamiltonian H0(k) with the same form as the non-interacting model but renormalized hoppings. In the topological Mott zero (TMZ) phase these zero bands have a nonzero N3,σ, which produces gapless charge-neutral zero modes at a boundary even though the single-particle excitation gap stays open and σxy = 0. The paper establishes bulk-boundary correspondence for both poles and zeros, including at junctions between TMBI and TMZ phases.

Load-bearing premise

The results rest on the truncation J(t)≈EΨ(t) of the equation of motion that keeps only holon and doublon operators in the basis; if that approximation misses a gap closing, the claimed topological phases, edge modes, and winding numbers are artifacts.

Editorial extensions

If this is right

  • If the TMBI claim is right, a paramagnetic half-filled Mott insulator with two orbitals can show a quantized anomalous Hall effect without any non-interacting band structure being topological at the same parameters.
  • If the TMZ claim is right, a gapped Mott insulator can host gapless boundary zero modes that carry no charge, leaving the Hall conductivity exactly zero despite a nonzero single-particle winding number.
  • The junction results imply that pole and zero edge modes are distinct objects: since poles carry charge and zeros do not, they cannot hybridize and gap out within a single-particle Green's-function description.
  • The phase diagram gives concrete parameter windows, such as Us=12.2t, M=4.36t for the TMBI and Us=13.71t, M=0.53t for the TMZ, where numerical or experimental emulators could look for these signatures.
  • The additive property of N3 means the winding of individual Hubbard bands or zero bands can be assigned separately, so the same formalism can classify partial fillings or doped Mott states.

Reading between the lines

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

  • The identification of Green's function zeros with an effective Hamiltonian H0(k) suggests that zeros in other multi-orbital Mott insulators might be readable as ordinary band topology of a charge-neutral 'zero' quasiparticle; this is a testable hypothesis beyond the Chern-Hubbard model.
  • Because the COM truncation is benchmarked only on the Hubbard dimer, a natural next check is a controlled comparison against cluster or quantum Monte Carlo results for the two-band model, with the phase boundaries in the Us–M diagram being the most likely place for the approximation to shift.
  • The physical ambiguity of placing the chemical potential inside the zero gap means the TMZ phase's nonzero N3 may be a statement about the Green's function rather than a thermodynamic phase; one way to sharpen it would be to define the zero winding through twisted boundary conditions or a charge probe.
  • In moiré materials with flat bands, the relevant energy ratio is interaction to bandwidth rather than to bare hopping, so the same holon-doublon mechanism could be realized with much smaller U/t than the values used here.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The manuscript studies the two-band Chern-Hubbard model at half-filling in the strong-coupling regime using the composite operator method (COM) in the two-pole holon/doublon basis with Roth decoupling. It reports two interaction-driven topological phases: a topological Mott band insulator (TMBI), in which the occupied Hubbard subbands acquire a nonzero winding number N3 and a quantized Hall conductivity, and a topological Mott zero (TMZ) phase, in which bands of Green's function zeros acquire a nonzero N3 while the system remains insulating. The paper supports these claims with bulk band structures, open-boundary spectra, π-flux probes, a TMBI-TMZ junction calculation, and a Streda-formula evaluation of the many-body Chern number. The effective zeros Hamiltonian H0(k) is explicitly presented as a conjecture, and the chemical-potential placement used to define N3 for zero bands is acknowledged to be ambiguous.

Significance. If the claims hold, the paper provides a concrete strong-coupling route to a Chern insulator in a two-orbital Hubbard model and a systematic framework for studying topological Green's function zeros, with possible relevance to moiré flat-band systems. The work is commendable for its internal consistency checks: fully self-consistent momentum-space and real-space COM solutions, a dimer benchmark, bulk-boundary correspondence checks for both poles and zeros, π-flux defect probes, and Streda-formula verification that the TMBI phase has Cσ=1 while TMZ has Cσ=0. The explicit caveats—the conjectural H0 and the ambiguous µ placement—are disclosed rather than hidden. The main limitation is that the central approximation is uncontrolled, and the benchmark supplied shows quantitative failure at the interaction strengths used.

major comments (3)
  1. [Appendix C, Fig. 7(b); Fig. 5] The dimer benchmark in Appendix C (Fig. 7(b)) shows that COM underestimates hybridization for U/t = 10, while the main phase diagram uses Us = 12.18t and Up = 13t. Since the topological transition in the TMBI phase is driven by holon-doublon hybridization (Fig. 1D), a systematic underestimate of this hybridization can shift the gap-closing/reopening points that define the phase boundaries in Fig. 5A, or in the worst case eliminate them. The statement in Appendix C that precise positions 'may shift' is not sufficient, because topological invariants change exactly at those positions. To support the claim that the exact Hubbard model hosts these phases, an independent benchmark—exact diagonalization or cluster/DMFT on finite systems, or a controlled expansion of the COM basis—is needed at the parameter values used in the main text.
  2. [Appendix A3; Section III B] The effective Hamiltonian H0(k) = Tr[E(k)ρ0(k)] in Eqs. (A6) and (A8) is explicitly conjectural. The TMZ phase and its zero-mode bulk-boundary correspondence rest on this object: the winding number is computed from the eigenvalues of H0, and the edge zero modes are identified from min eig G. Although the numerical agreement between eigenvectors of H0 and zero modes of G is reassuring, it does not establish that H0 is the correct low-energy description of the zeros; the ansatz for |ψ0(k)⟩ in Eq. (A7) is not derived from a controlled expansion. Please provide at least a derivation in the atomic limit with explicit first-order corrections in t/U, or an independent calculation of the zero-band topology.
  3. [Section III B 1; Eq. (6)] The definition of N3 for the zero bands requires placing µ in the gap of zeros; the paper states that this choice is 'physically ambiguous but mathematically allowed.' Since different placements between the two zero bands give different N3 (the upper and lower zero bands have opposite winding), the TMZ classification is not unique. The phase diagram in Fig. 5B should either identify a physical criterion for fixing µ (e.g., a Luttinger-surface or ground-state criterion) or demonstrate that all statements about edge zero modes are independent of this choice. Without this, the existence of a distinct TMZ phase is not uniquely defined.
minor comments (6)
  1. [Fig. 2 caption and text] The text refers to 'Fig. (2.c/d)', but the figure panels are labeled (A) and (B); please correct the labels or the text.
  2. [Appendix C, Fig. 7] Both panels in Fig. 7 are labeled '(b)'; the atomic-limit panel should be '(a)' and the finite-hopping panel '(b)'.
  3. [Section II, paragraph after Eq. (1)] The sentence 'Here N is is the total number of sites' contains a duplicated 'is'.
  4. [Section III C, paragraph near Fig. 5] The phrase 'quantum anamolous Hall' should read 'anomalous Hall'.
  5. [Appendix B 6, Eq. (B81)] The final sentence of this paragraph, 'if zeros are not taking into account in the computation of N3[G], we have N3[G] = N3[G]', appears to contain a typo or an undefined comparison; please state precisely which invariant is being compared.
  6. [Appendix A3 b] The phrase 'the enerfy of the zerors' should be corrected to 'the energy of the zeros'.

Circularity Check

2 steps flagged · score 3.0 of 10

Pole topology is derived self-consistently and benchmarked; the zeros-as-bound-pairs claim is a definitional rewriting of the COM energy matrix, and the TMZ winding is explicitly contingent on the chosen chemical-potential placement.

  1. self definitional [Appendix A 3 (Eqs. A5-A8) and abstract]
    "Conjecture : The dispersion of the electronic Green’s function zeros are given by the eigenvalues of the following Hamiltonian H0(k) = Tr{η,ξ} [E(k)ˆρ0(k)] ... The eigenvalues of the H0 reproduces the band of Green’s function zeros in Eq. (A4)."

    H0 is constructed from the same E(k) matrix that defines the composite Green's function G = (ω−E)^{-1}I, with ρ0 chosen as an equal-weight holon/doublon superposition. That H0's eigenvalues reproduce the zeros of G is therefore a rearrangement of the input E(k), not an independent derivation. The abstract's statement that 'Green function zeros manifest as the tightly bound pairs' restates this constructed H0, so the physical interpretation is built in by definition rather than derived from external data.

  2. self definitional [Section III.B.1 (paragraph after Fig. 3)]
    "The filling of a specific GFZ band by a particular choice of µ remains physically ambiguous but is mathematically allowed. However, when the zero bands acquire a finite winding number due to the positioning of the chemical potential between them, we refer to this phase as the Topological Mott Zero (TMZ)."

    The TMZ winding N3 is not an output fixed by the Hamiltonian alone: the same Green's function can yield different N3 depending on where µ is placed inside the gap of zeros. The paper defines the TMZ phase as the situation in which the chosen µ placement produces a finite zero-band winding, so the existence of this phase is contingent on a convention rather than derived from a physical filling. The authors are transparent about the ambiguity, and this step does not affect the pole winding, the edge spectra, or the Hall-conductivity checks.

full rationale

The main topological claim for the occupied single-particle excitation bands (TMBI) is obtained from self-consistent COM Green's functions and is not circular: the energy matrix E = MI^{-1} is an approximation, not a fit to the target winding, and the dimer benchmark in Appendix C plus the Streda-formula Hall check in Appendix E provide independent, external validation. The self-citations (Refs. 23, 45, 46) are methodological and are not invoked as load-bearing uniqueness theorems. The two genuine reduction-by-definition aspects are confined to the zeros sector: the H0 'bound holon-doublon pair' Hamiltonian is constructed from the same E(k) that generates G, making the reproduction of zero bands tautological, and the TMZ winding explicitly depends on placing the chemical potential between zero bands, a choice the paper admits is physically ambiguous. Because the central TMBI derivation and the concrete edge-zero-mode spectra have independent content, the overall circularity is partial rather than total.

Assumptions & free parameters 3 free parameters · 6 assumptions · 2 invented entities

The central claims rely on the COM equation-of-motion truncation, the paramagnetic assumption, Roth decoupling, and a conjectured zeros Hamiltonian. The free choices of hole doping and of the chemical potential window for the zero-band winding directly affect the computed topological invariants, so the phase diagram cannot be considered a parameter-free prediction.

free parameters (3)
  • Hole doping n=1.99 used to reach self-consistency = n=1.99, with mu then fixed at half-filling
    Sec. III states that small hole doping was introduced 'to mitigate convergence issues of fixing the chemical potential in a large Mott gap'; the resulting self-consistent parameters in Table I depend on this choice, and exact half-filling could shift the phase boundaries.
  • Chemical potential window for zero-band winding = mu values in Table I, e.g. 5.94t and 5.88t for the TMZ phases
    In Sec. III B 1 the authors place mu inside the gap of zeros to compute N3 and explicitly say the filling of a specific GFZ band by the choice of mu is physically ambiguous. Different mu placements change the zero-band winding, so this is a choice, not a unique prediction.
  • COM self-consistent parameters (n_alpha, e_alpha, e_sp, p_alpha,beta) = Table I values, e.g. ns=1.14, np=0.86 in the TMBI phase
    These are solved self-consistently rather than fitted to external data, but they act as free inputs to the E-matrix and therefore to all topological invariants. They are listed because the central phase diagram cannot be checked without them.
assumptions (6)
  • domain assumption Equation-of-motion truncation J(t) = [H, Psi](t) approximately E Psi(t)
    Used in Eq. (4) to write the composite Green's function as (omega - E)^{-1} I; this is the central COM approximation and the basis for the entire calculation.
  • domain assumption Paramagnetic, spin-degenerate solution with decoupled spin sectors
    Sec. II B; actual invariants are taken as twice the spin-sector values. Half-filled Mott systems can develop antiferromagnetic order, which the paper does not analyze, though the authors acknowledge this in Sec. IV A.
  • domain assumption Infinite lifetime of holon and doublon excitations in the paramagnetic Mott phase
    Used in Sec. III A 1 to justify applying the non-interacting inversion-eigenvalue criterion Eq. (8) to the interacting COM bands; relies on Ref. [59].
  • domain assumption Roth decoupling for two-point correlation functions
    Appendix B5; the pss, ppp, and psp parameters are obtained from this decoupling scheme. It is an uncontrolled approximation for the two-band model.
  • ad hoc to paper Conjectured zeros Hamiltonian H0(k) = Tr[E(k) rho0(k)]
    Eqs. (A6) and (A8) are explicitly called a conjecture in Appendix A3; the interpretation of zeros as tightly bound holon-doublon pairs rests on this conjecture, and no independent derivation is provided.
  • ad hoc to paper Chemical potential can be placed arbitrarily within the excitation gap when computing N3 of zeros
    Sec. III B 1; the mathematical definition of the zero-band winding depends on this placement, which the authors admit is not physically determined.
invented entities (2)
  • Effective zeros Hamiltonian H0(k)
    purpose: To assign a tight-binding Hamiltonian to the bands of Green's function zeros and to define their topological character
    Introduced as a conjecture in Appendix A3, Eqs. (A6) and (A8); it reproduces the zero dispersion by construction and has no falsifiable handle outside the paper.
  • Tightly bound holon-doublon pair interpretation of zeros
    purpose: Identifies Green's function zeros as bound composites of holons and doublons
    The claim is inferred from the conjectured H0 decomposition, not from a direct calculation of a two-particle bound-state wavefunction or binding energy.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Topological charge excitations and Green's function zeros in paramagnetic Mott insulators." pith.science (2026). https://pith.science/paper/FJKKQF55

@misc{pith2026241213302,
  author       = {Pith},
  title        = {Pith review of: Topological charge excitations and Green's function zeros in paramagnetic Mott insulators},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FJKKQF55}},
  note         = {Machine review of arXiv:2412.13302}
}
read the original abstract

We investigate the emergence of topological features in the charge excitations of Mott insulators in the Chern-Hubbard model. In the strong correlation regime, treating electrons as the sum of holons and doublons excitations, we compute the topological phase diagram of Mott insulators at half-filling using composite operator formalism. The Green function zeros manifest as the tightly bound pairs of such elementary excitations of the Mott insulators. Our analysis examines the winding number associated with the occupied Hubbard bands and the band of Green's function zeros. We show that both the poles and zeros show gapless states and zeros, respectively, in line with bulk-boundary correspondence. The gapless edge states emerge in a junction geometry connecting a topological Mott band insulator and a topological Mott zeros phase. These include an edge electronic state that carries a charge and a charge-neutral gapless zero mode. Our study is relevant to several twisted materials with flat bands where interactions play a dominant role.

Figures

Figures reproduced from arXiv: 2412.13302 by the authors.

Figure 1
Figure 1. FIG. 1. Hubbard subbands along the path [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Low energy charge excitations of two-band Chern-Hubbard [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Green function zeros are shown for the following cases : [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The minimum eigenvalue of the single particle electronic [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. (A) Displays the [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The minimum (left column) and maximum (right column) [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Comparison of [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. The minimum (left column) and maximum (right column) eigenvalue of the single particle Green function [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Variation of the electron density [PITH_FULL_IMAGE:figures/full_fig_p019_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Response to a [PITH_FULL_IMAGE:figures/full_fig_p020_10.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

98 extracted references · 76 canonical work pages

  1. [1]

    Single-electron excitation spectrum FIG. 1. Hubbard subbands along the path Γ → X → M → Γ for Us = 12 .2t: (A) M = −0.28t, (B) M = 4 .36t, and (C) M = 6.08t. In the left column, colors represent the orbital character of each band, while in the right column, colors denote the holon- doublon excitation character. Bands below the black dotted line in- dicate...

  2. [2]

    Bulk boundary correspondence of poles Since N3,σ is a single-particle topological invariant quan- tized without symmetry protection, it cannot change without the single-particle gap closing. Consequently, the spectrum must be gapless under open boundary conditions if the sys- tem possesses a non-zero winding of the occupied bands or at a junction between ...

  3. [3]

    Dispersion of Green function zeros FIG. 3. Green function zeros are shown for the following cases : (A/B) Us = 13.7t M= −0.48t, (C/D) M = 0.53t Us = 13.7t and (E/F) M = 0 .53t Us = 7 .6t. The left side displays Det [G(k, ω)] along the path ΓXM Γ. The right side shows the orbital character of the electronic Green function zero modes. In the non-zero windin...

  4. [4]

    Bulk boundary correspondence of Greens function zeros Since the zeros band can carry a non-zero N3 invariant, there exists a ‘bulk-boundary’ correspondence for GFZ, simi- lar to the well-known correspondence for poles. In Fig. (4 A) and Fig. (4 B), we show the minimum eigenvalue of G(ω, ky) with open boundary condition in the MI phase and the TMZ phase re...

  5. [5]

    F. D. M. Haldane, Model for a quantum hall effect with- out landau levels: Condensed-matter realization of the ”parity anomaly”, Phys. Rev. Lett. 61, 2015 (1988)

    1988

  6. [6]

    C. L. Kane and E. J. Mele, Z2 topological order and the quan- tum spin hall effect, Phys. Rev. Lett. 95, 146802 (2005)

    2005

  7. [7]

    B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Quantum spin hall effect and topological phase transition in hgte quantum wells, Science 314, 1757 (2006)

    2006

  8. [8]

    L. Fu, C. L. Kane, and E. J. Mele, Topological insulators in three dimensions, Phys. Rev. Lett. 98, 106803 (2007)

    2007

Show all 98 references
  1. [9]

    J. E. Moore and L. Balents, Topological invariants of time- reversal-invariant band structures, Phys. Rev. B 75, 121306 (2007)

    2007

  2. [10]

    Altland and M

    A. Altland and M. R. Zirnbauer, Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures, Phys. Rev. B 55, 1142 (1997)

    1997

  3. [11]

    Qi and S.-C

    X.-L. Qi and S.-C. Zhang, Topological insulators and supercon- ductors, Rev. Mod. Phys. 83, 1057 (2011)

    2011

  4. [12]

    M. Z. Hasan and C. L. Kane, Colloquium: Topological insula- tors, Rev. Mod. Phys. 82, 3045 (2010)

    2010

  5. [13]

    Bradlyn, L

    B. Bradlyn, L. Elcoro, J. Cano, M. G. Vergniory, Z. Wang, C. Felser, M. I. Aroyo, and B. A. Bernevig, Topological quan- tum chemistry, Nature 547, 298 (2017)

    2017

  6. [14]

    Kruthoff, J

    J. Kruthoff, J. De Boer, J. Van Wezel, C. L. Kane, and R.- J. Slager, Topological classification of crystalline insulators through band structure combinatorics, Physical Review X 7, 041069 (2017)

    2017

  7. [15]

    Dzyaloshinskii, Some consequences of the luttinger theorem: The luttinger surfaces in non-fermi liquids and mott insulators, Phys

    I. Dzyaloshinskii, Some consequences of the luttinger theorem: The luttinger surfaces in non-fermi liquids and mott insulators, Phys. Rev. B 68, 085113 (2003)

    2003

  8. [16]

    K. B. Dave, P. W. Phillips, and C. L. Kane, Absence of lut- tinger’s theorem due to zeros in the single-particle green func- tion, Phys. Rev. Lett. 110, 090403 (2013)

    2013

  9. [17]

    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)

    1965

  10. [18]

    Hatsugai and M

    Y . Hatsugai and M. Kohmoto, Exactly solvable model of corre- lated lattice electrons in any dimensions, Journal of the Physical Society of Japan 61, 2056 (1992)

    1992

  11. [19]

    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)

    2024

  12. [20]

    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)

    2024

  13. [21]

    P. W. Phillips, L. Yeo, and E. W. Huang, Exact theory for super- conductivity in a doped mott insulator, Nature Physics16, 1175 9 (2020)

    2020

  14. [22]

    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. Series A. Mathemat- ical and Physical Sciences 276, 238 (1963)

    1963

  15. [23]

    Beenen and D

    J. Beenen and D. M. Edwards, Superconductivity in the two- dimensional hubbard model, Phys. Rev. B 52, 13636 (1995)

    1995

  16. [24]

    Avella, F

    A. Avella, F. Mancini, D. Villani, L. Siurakshina, and V . Y . Yushankhai, The hubbard model in the two-pole approximation, International Journal of Modern Physics B 12, 81 (1998)

    1998

  17. [25]

    T. D. Stanescu, I. Martin, and P. Phillips, dx2-y2 pairing of composite excitations in the two-dimensional hubbard model, Physical Review B 62, 4300 (2000)

    2000

  18. [26]

    Avella and F

    A. Avella and F. Mancini, The composite operator method (com), in Strongly Correlated Systems: Theoretical Methods (Springer, 2011) pp. 103–141

    2011

  19. [27]

    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 Matter 36, 255601 (2024)

    2024

  20. [28]

    T. Li, S. Jiang, B. Shen, Y . Zhang, L. Li, Z. Tao, T. Devakul, K. Watanabe, T. Taniguchi, L. Fu, J. Shan, and K. F. Mak, Quantum anomalous hall effect from intertwined moir ´e bands, Nature 600, 641 (2021)

    2021

  21. [29]

    Serlin, C

    M. Serlin, C. L. Tschirhart, H. Polshyn, Y . Zhang, J. Zhu, K. Watanabe, T. Taniguchi, L. Balents, and A. F. Young, Intrin- sic quantized anomalous hall effect in a moir ´e heterostructure, Science 367, 900 (2020)

    2020

  22. [30]

    G. Chen, A. L. Sharpe, E. J. Fox, Y .-H. Zhang, S. Wang, L. Jiang, B. Lyu, H. Li, K. Watanabe, T. Taniguchi, Z. Shi, T. Senthil, D. Goldhaber-Gordon, Y . Zhang, and F. Wang, Tun- able correlated chern insulator and ferromagnetism in a moir ´e superlattice, Nature 579, 56 (2020)

    2020

  23. [31]

    Yoshida, R

    T. Yoshida, R. Peters, S. Fujimoto, and N. Kawakami, Topolog- ical antiferromagnetic phase in a correlated bernevig-hughes- zhang model, Phys. Rev. B 87, 085134 (2013)

    2013

  24. [32]

    Amaricci, J

    A. Amaricci, J. C. Budich, M. Capone, B. Trauzettel, and G. Sangiovanni, First-order character and observable signatures of topological quantum phase transitions, Phys. Rev. Lett. 114, 185701 (2015)

    2015

  25. [33]

    Hohenadler and F

    M. Hohenadler and F. F. Assaad, Correlation effects in two- dimensional topological insulators, Journal of Physics: Con- densed Matter 25, 143201 (2013)

    2013

  26. [34]

    Y . Tada, R. Peters, M. Oshikawa, A. Koga, N. Kawakami, and S. Fujimoto, Correlation effects in two-dimensional topological insulators, Phys. Rev. B 85, 165138 (2012)

    2012

  27. [35]

    Zheng, G.-M

    D. Zheng, G.-M. Zhang, and C. Wu, Particle-hole symmetry and interaction effects in the kane-mele-hubbard model, Phys. Rev. B 84, 205121 (2011)

    2011

  28. [36]

    S.-L. Yu, X. C. Xie, and J.-X. Li, Mott physics and topological phase transition in correlated dirac fermions, Phys. Rev. Lett. 107, 010401 (2011)

    2011

  29. [37]

    Hohenadler, Z

    M. Hohenadler, Z. Y . Meng, T. C. Lang, S. Wessel, A. Mura- matsu, and F. F. Assaad, Quantum phase transitions in the kane- mele-hubbard model, Phys. Rev. B 85, 115132 (2012)

    2012

  30. [38]

    Bercx, M

    M. Bercx, M. Hohenadler, and F. F. Assaad, Kane-mele- hubbard model on the π-flux honeycomb lattice, Physical Re- view B 90, 075140 (2014)

    2014

  31. [39]

    Lee, Effects of interaction on quantum spin hall insula- tors, Phys

    D.-H. Lee, Effects of interaction on quantum spin hall insula- tors, Phys. Rev. Lett. 107, 166806 (2011)

    2011

  32. [40]

    T. I. Vanhala, T. Siro, L. Liang, M. Troyer, A. Harju, and P. T¨orm¨a, Topological phase transitions in the repulsively in- teracting haldane-hubbard model, Physical Review Letters116, 225305 (2016)

    2016

  33. [41]

    I. S. Tupitsyn and N. V . Prokof’ev, Phase diagram topology of the haldane-hubbard-coulomb model, Physical Review B 99, 121113 (2019)

    2019

  34. [42]

    W.-X. He, R. Mondaini, H.-G. Luo, X. Wang, and S. Hu, Phase transitions in the haldane-hubbard model, Phys. Rev. B 109, 035126 (2024)

    2024

  35. [43]

    P. Mai, J. Zhao, B. E. Feldman, and P. W. Phillips, 1/4 is the new 1/2 when topology is intertwined with mottness, Nature Communications 14, 5999 (2023)

    2023

  36. [44]

    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 Communications 14, 7531 (2023)

    2023

  37. [45]

    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)

    2024

  38. [46]

    T. L. Hughes, E. Prodan, and B. A. Bernevig, Inversion- symmetric topological insulators, Physical Review B 83, 245132 (2011)

    2011

  39. [47]

    Y . Tang, L. Li, T. Li, Y . Xu, S. Liu, K. Barmak, K. Watan- abe, T. Taniguchi, A. H. MacDonald, J. Shan, and K. F. Mak, Simulation of hubbard model physics in wse2/ws2 moir´e super- lattices, Nature 579, 353 (2020)

    2020

  40. [48]

    X.-L. Qi, T. L. Hughes, and S.-C. Zhang, Topological field theory of time-reversal invariant insulators, Physical Review B—Condensed Matter and Materials Physics 78, 195424 (2008)

    2008

  41. [49]

    Pangburn, L

    E. Pangburn, L. Haurie, S. Burdin, C. P ´epin, and A. Banerjee, Spontaneous orbital selective mott phase in the two band hub- bard model, arXiv preprint arXiv:2407.11126 (2024)

    2024 arXiv

  42. [50]

    Banerjee, E

    A. Banerjee, E. Pangburn, C. Mahato, A. Ghosal, and C. P´epin, Charge density wave solutions of the hubbard model in the com- posite operator formalism (2024), arXiv:2410.09903 [cond- mat.str-el]

    2024 arXiv

  43. [51]

    Gurarie, Single-particle green’s functions and interacting topological insulators, Physical Review B 83, 085426 (2011)

    V . Gurarie, Single-particle green’s functions and interacting topological insulators, Physical Review B 83, 085426 (2011)

    2011

  44. [52]

    He, H.-Q

    Y .-Y . He, H.-Q. Wu, Z. Y . Meng, and Z.-Y . Lu, Topological in- variants for interacting topological insulators. i. efficient numer- ical evaluation scheme and implementations, Physical Review B 93, 195163 (2016)

    2016

  45. [53]

    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, Physical Review B 93, 195164 (2016)

    2016

  46. [54]

    J. Zhao, P. Mai, B. Bradlyn, and P. Phillips, Failure of topo- logical invariants in strongly correlated matter, Phys. Rev. Lett. 131, 106601 (2023)

    2023

  47. [55]

    Streda, Theory of quantised hall conductivity in two di- mensions, Journal of Physics C: Solid State Physics 15, L717 (1982)

    P. Streda, Theory of quantised hall conductivity in two di- mensions, Journal of Physics C: Solid State Physics 15, L717 (1982)

    1982

  48. [56]

    D. R. Hofstadter, Energy levels and wave functions of bloch electrons in rational and irrational magnetic fields, Physical re- view B 14, 2239 (1976)

    1976

  49. [57]

    F. F. Assaad, M. Bercx, and M. Hohenadler, Topological invari- ant and quantum spin models from magnetic π fluxes in corre- lated topological insulators, Phys. Rev. X 3, 011015 (2013)

    2013

  50. [58]

    Juriˇci´c, A

    V . Juriˇci´c, A. Mesaros, R.-J. Slager, and J. Zaanen, Universal probes of two-dimensional topological insulators: dislocation and π flux, Physical Review Letters 108, 106403 (2012)

    2012

  51. [59]

    Slager, The translational side of topological band insula- tors, Journal of Physics and Chemistry of Solids128, 24 (2019)

    R.-J. Slager, The translational side of topological band insula- tors, Journal of Physics and Chemistry of Solids128, 24 (2019)

    2019

  52. [60]

    Schindler, S

    F. Schindler, S. S. Tsirkin, T. Neupert, B. Andrei Bernevig, and B. J. Wieder, Topological zero-dimensional defect and flux states in three-dimensional insulators, Nature Communications 10 13, 5791 (2022)

    2022

  53. [61]

    Fu and C

    L. Fu and C. L. Kane, Topological insulators with inversion symmetry, Phys. Rev. B76, 045302 (2007)

    2007

  54. [62]

    Alexandradinata, X

    A. Alexandradinata, X. Dai, and B. A. Bernevig, Wilson-loop characterization of inversion-symmetric topological insulators, Physical Review B 89, 155114 (2014)

    2014

  55. [63]

    L. M. Roth, Electron correlation in narrow energy bands. i. the two-pole approximation in a narrow s band, Phys. Rev. 184, 451 (1969)

    1969

  56. [64]

    C.-K. Chiu, J. C. Teo, A. P. Schnyder, and S. Ryu, Classifica- tion of topological quantum matter with symmetries, Reviews of Modern Physics 88, 035005 (2016)

    2016

  57. [65]

    Seki and S

    K. Seki and S. Yunoki, Topological interpretation of the lut- tinger theorem, Physical Review B 96, 085124 (2017)

    2017

  58. [66]

    A. B. Harris and R. V . Lange, Single-particle excitations in nar- row energy bands, Phys. Rev.157, 295 (1967)

    1967

  59. [67]

    Sinha and B

    S. Sinha and B. Bradlyn, Computing the invariant in two-dimensional strongly-correlated systems, arXiv preprint arXiv:2409.12120 (2024)

    2024 arXiv

  60. [68]

    P. Mai, J. Zhao, T. A. Maier, B. Bradlyn, and P. W. Phillips, Topological phase transition without single particle gap clos- ing in strongly correlated systems, Phys. Rev. B 110, 075105 (2024)

    2024

  61. [69]

    Devakul and L

    T. Devakul and L. Fu, Quantum anomalous hall effect from inverted charge transfer gap, Physical Review X 12, 021031 (2022)

    2022

  62. [70]

    Hirsch, Superconductors that change color when they be- come superconducting, Physica C: Superconductivity 201, 347 (1992)

    J. Hirsch, Superconductors that change color when they be- come superconducting, Physica C: Superconductivity 201, 347 (1992)

    1992

  63. [71]

    P. Mai, B. E. Feldman, and P. W. Phillips, Topological mott in- sulator at quarter filling in the interacting haldane model, Phys- ical Review Research 5, 013162 (2023)

    2023

  64. [72]

    S. R. Hassan, G. Prakash, N. S. Vidhyadhiraja, and T. V . Ra- makrishnan, Strong local bosonic fluctuations: The key to understanding strongly correlated metals, Phys. Rev. B 110, 075106 (2024)

    2024

  65. [73]

    Odashima, A

    S. Odashima, A. Avella, and F. Mancini, High-order correlation effects in the two-dimensional hubbard model, Physical Review B 72, 205121 (2005)

    2005

  66. [74]

    Prelov ˇsek, J

    P. Prelov ˇsek, J. Kokalj, Z. Lenar ˇciˇc, and R. H. McKenzie, Holon-doublon binding as the mechanism for the mott transi- tion, Physical Review B 92, 235155 (2015)

    2015

  67. [75]

    S. Roy, S. Pervaiz, T. Paiva, and N. Trivedi, Signatures of metal to insulator crossover in the repulsive fermi hubbard model through static correlations, arXiv preprint arXiv:2403.13054 (2024)

    2024 arXiv

  68. [76]

    G. G. Blesio, L. O. Manuel, P. Roura-Bas, and A. A. Ali- gia, Topological quantum phase transition between fermi liquid phases in an anderson impurity model, Phys. Rev. B98, 195435 (2018)

    2018

  69. [77]

    non-landau

    R. ˇZitko, G. G. Blesio, L. O. Manuel, and A. A. Aligia, Iron ph- thalocyanine on au(111) is a “non-landau” fermi liquid, Nature Communications 12, 6027 (2021)

    2021

  70. [78]

    Fabrizio, Emergent quasiparticles at luttinger surfaces, Na- ture Communications 13, 1561 (2022)

    M. Fabrizio, Emergent quasiparticles at luttinger surfaces, Na- ture Communications 13, 1561 (2022)

    2022

  71. [79]

    Skolimowski and M

    J. Skolimowski and M. Fabrizio, Luttinger’s theorem in the presence of luttinger surfaces, Physical Review B 106, 045109 (2022)

    2022

  72. [80]

    Blason and M

    A. Blason and M. Fabrizio, Unified role of green’s function poles and zeros in correlated topological insulators, Physical Review B 108, 125115 (2023)

    2023

  73. [81]

    Fabrizio, Spin-liquid insulators can be landau’s fermi liq- uids, Physical Review Letters 130, 156702 (2023)

    M. Fabrizio, Spin-liquid insulators can be landau’s fermi liq- uids, Physical Review Letters 130, 156702 (2023)

    2023

  74. [82]

    Blason, I

    A. Blason, I. Pasqua, M. Ferrero, and M. Fabrizio, Luttinger surface dominance and fermi liquid behavior of topological kondo insulators smb 6 and ybb 12, Physical Review B 110, 235115 (2024)

    2024

  75. [83]

    Pasqua, A

    I. Pasqua, A. Blason, and M. Fabrizio, Exciton condensation driven by bound states of green’s function zeros, Phys. Rev. B 110, 125144 (2024)

    2024

  76. [84]

    Dzyaloshinskii, Some consequences of the luttinger theorem: The luttinger surfaces in non-fermi liquids and mott insulators, Physical Review B 68, 085113 (2003)

    I. Dzyaloshinskii, Some consequences of the luttinger theorem: The luttinger surfaces in non-fermi liquids and mott insulators, Physical Review B 68, 085113 (2003)

    2003

  77. [85]

    Bollmann, C

    S. Bollmann, C. Setty, U. F. Seifert, and E. J. K ¨onig, Topo- logical green’s function zeros in an exactly solved model and beyond, arXiv preprint arXiv:2312.14926 (2023)

    2023 arXiv

  78. [86]

    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, Physical Review Letters 131, 236601 (2023)

    2023

  79. [87]

    Pavarini, E

    E. Pavarini, E. Koch, and F. J. G. G. I. for Advanced Simulation, Simulating correlations with computers. Lecture notes of the autumn school on correlated electrons 2021 , V ol. 11 (Institute for Advanced Simulation, 2021)

    2021

  80. [88]

    Herzog-Arbeitman, Z.-D

    J. Herzog-Arbeitman, Z.-D. Song, N. Regnault, and B. A. Bernevig, Hofstadter topology: Noncrystalline topological ma- terials at high flux, Phys. Rev. Lett. 125, 236804 (2020)

    2020

  81. [89]

    Y . Ran, A. Vishwanath, and D.-H. Lee, Spin-charge separated solitons in a topological band insulator, Physical Review Letters 101, 086801 (2008). Appendix A: Green function zeros in composite operator method

    2008

  82. [90]

    Single-orbital Hubbard Model For single band Hubbard model the dispersion of Green function zeros at a fillingn = 1 can be readily obtained from Ref. [23]. At half-filled case, e = 0 and hence the M-matrix becomes 2 × 2 matrix and is given by M(k) = −µ/2 − γ(k)p −γ(k)(1/2 − p)...

  83. [91]

    Two-orbital system The dispersion of the zeros are also solvable in the case of the Chern-Hubbard model where the E-matrix is a 4 × 4 matrix for each k. Similar argument than the previous section leads to two solutions for det G(k, ω) = 0 at each k, ω± 0 (k) = 1 4 ± h (E11ns −...

  84. [92]

    Single orbital system Let us assume we can prepare the system in a state which is an equal superposition state of the doublons and holons for every crystal momentum

    Conjecture of a Hamiltonian describing Green function zeroes a. Single orbital system Let us assume we can prepare the system in a state which is an equal superposition state of the doublons and holons for every crystal momentum. The state is given by |ψ0(k)⟩ = 1√ 2 (|ξ(k)⟩ − ...

  85. [93]

    We first choose the following 4N-compoment basis for the composite operator Ψi = (

    Non-uniform systems The study of local probes requires a real-space formulation of the composite operator formalism. We first choose the following 4N-compoment basis for the composite operator Ψi = (. . . , ξisσ, ηisσ, ξipσ, ηipσ, . . .)T (B1) For completeness, the non-zero el...

  86. [94]

    Note that to evaluate the parameter nα and eαβ we only need the single particle on-site and nearest neighbor correlation functions

    Correlation function and self-consistency The M-matrix and the I-matrix depends on initally unknown parameters ( eαβ, pαβ, nα, µ) that needs to be determined self consistently. Note that to evaluate the parameter nα and eαβ we only need the single particle on-site and nearest ...

  87. [95]

    (B27) by using a spectral decomposition

    Correlation function computation We can simplify theω integration in the fluctuation-dissipation theorem of Eq. (B27) by using a spectral decomposition. First, the E- matrix can be diagonalize E = RDR−1, (B28) Where R is the matrix of right eigenvectors of E and D is the diago...

  88. [96]

    Self-consistent equations in terms of correlation function We present the expressions for the single-particle self-consistent parameters directly in terms of correlation functions. ns(i) = 2 1 − C 11 0 (i) − C 22 0 (i) − C 12 0 (i) − C 21 0 (i) (B32) np(i) = 2 1 − C 33 0 (i) −...

  89. [97]

    This allows us to express p in terms of both on-site and intersite correlations

    Roth decoupling We use the Roth decoupling scheme [59] to compute two-point correlation functions, including density-density, spin-spin, and pair-pair correlations, as described in Eq.(B80). This allows us to express p in terms of both on-site and intersite correlations. The d...

  90. [98]

    Uniform system Thus, the I-matrix is diagonal. For the uniform system the diagonal elements are given by I = diag [(1 − ns/2, ns/2, 1 − np/2, np/2)] , (B59) where we have defined average orbital electron density as nα = (1/N) P i,σ⟨ˆni,α,σ⟩. The uniform and C4 symmetric M-matr...

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.