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arxiv: 2605.20321 · v1 · pith:I7ZDTL2Ynew · submitted 2026-05-19 · ✦ hep-th · cond-mat.str-el

Poles-zeros duality in semi-holographic Mott insulators

Thomas K\"ogel , Alessio Caddeo , Amelie Pitters , Francesca Paoletti , Lorenzo Crippa , Giorgio Sangiovanni , Ren\'e Meyer , Johanna Erdmenger This is my paper

Pith reviewed 2026-05-21 01:47 UTC · model grok-4.3

classification ✦ hep-th cond-mat.str-el
keywords semi-holographic Mott insulatorspoles-zeros dualityGreen's function zerosholographic self-energycomposite fermionsMott transitionspectral function
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The pith

A semi-holographic model transfers poles-zeros duality from a holographic composite fermion to a fundamental fermion via hybridization.

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

The paper proposes a semi-holographic construction for Mott insulators in which a fundamental fermion hybridizes with a composite fermion arising from a large-N strongly interacting holographic sector. This hybridization produces a self-energy whose poles generate zeros in the Green's function of the fundamental fermion, with those poles tied to collective many-body excitations in the holographic sector. The model computes the spectral function to separate metallic and Mott-insulating regimes and reinterprets the duality through the choice of standard versus alternative quantization in the bulk. A sympathetic reader would care because the construction supplies a concrete holographic mechanism for the zeros observed during Mott transitions in condensed-matter systems.

Core claim

Within the holographic framework at large N, the Green's function of the composite fermion naturally exhibits a poles-zeros duality. Zeros of the Green's function are caused by the poles of the self-energy that correspond to collective many-body excitations of the holographic strongly interacting sector. The duality transfers to the fundamental fermion through hybridization, and the freedom to choose between standard and alternative quantization supplies a well-defined bulk picture of the same duality.

What carries the argument

Hybridization of the fundamental fermion with the holographic composite fermion, which generates the self-energy whose poles produce the zeros.

Load-bearing premise

The Green's function of the composite fermion in the large-N holographic sector naturally exhibits poles-zeros duality that can be transferred to the fundamental fermion via hybridization.

What would settle it

An explicit large-N calculation of the composite-fermion Green's function that fails to place zeros precisely at the poles of the self-energy would falsify the claimed duality mechanism.

Figures

Figures reproduced from arXiv: 2605.20321 by Alessio Caddeo, Amelie Pitters, Francesca Paoletti, Giorgio Sangiovanni, Johanna Erdmenger, Lorenzo Crippa, Ren\'e Meyer, Thomas K\"ogel.

Figure 1
Figure 1. Figure 1: Plot of the logarithm of |ΣR,11(ω, k = 0, η = 5)| (blue) and |ΣR,11(ω, k = 0, η = −5)| (red) over frequency ω at k = 0. As predicted by Eq. (2.38), poles (zeros) at η = 5 are mapped into zeros (poles) at η = −5. The self-energy, related to the holographic correlator GR by Eq. (2.6), goes to a constant at large ω, consistently with the discussion in [51]. Thus, the Green’s function GR = iαfSγ 0 , in our bas… view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of log | det GR(ω, k, η)| for opposite-sign values of the bulk coupling, η = 5 (metallic, in panel (a)) and η = −5 (Mott insulating, in panel (b)). Bright yellow regions indicate peaks in the quantity, while dark purple regions correspond to zeros. The horizontal dashed lines represent the Fermi level which is ωF ≈ −1.2 for the metallic phase (left) while it is fixed in the middle of the gap, i.… view at source ↗
Figure 3
Figure 3. Figure 3: Plot of log| det GR(ω, k, η)| at k = 0 over ω deep in the Mott and metallic phase at η = 5 and η = −5 respectively. The zeros and the poles can be seen to match to a high level of accuracy. The gap in the Mott phase, determined from the edges of the spectral density ρ(ω, k) at k = 0, is here of size ∆gap = 6.82 in units of µ/√ 3, and is marked by the grey dashed vertical lines. The isolated, low-energy zer… view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of log det|GR(k = 0, ω)| (blue curves) and log |ΣR,11(k = 0, ω)| (red curves) at η = ±5. The dashed gray lines indicate the edges of the gap in the Mott phase, while the blue dashed line marks the location of the Fermi level in the metallic phase. 19 [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: For negative values of η, the system is a Mott insulator and here we plot its gap size as a function of η < 0. The gap opens at η = −0.17 for the cutoff 10−2 and at η = −0.51 for the 10−5 cutoff. The datapoints are determined from the average of the result for the gap for the two different cutoffs, while the error bars are given by the deviation from the average. For larger negative values of η the two cri… view at source ↗
Figure 6
Figure 6. Figure 6: Plots of the real (blue) and imaginary (red) part of [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Plots of the real (blue) and imaginary part (red) of [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗
read the original abstract

Inspired by the poles-zeros duality of Green's functions that appears in transitions into Mott-insulating phases in strongly correlated condensed matter systems, we propose a semi-holographic approach to Mott insulators. In this model, a fundamental fermion is coupled to a large-$N$, strongly interacting sector that generates a self-energy for the fundamental fermion's Green's function. This coupling amounts to a hybridization of the fundamental fermion with a strongly correlated fermionic composite. Within the holographic framework, at large $N$, the Green's function of the composite fermion naturally exhibits a poles-zeros duality. Zeros of the Green's function are caused by the poles of the self-energy that correspond to collective many-body excitations of the holographic strongly interacting sector. We calculate the spectral function of the fundamental fermion, from which we characterize the semi-holographic metallic and the Mott-insulating phases. In addition to the new physical interpretation of the zeros, our analysis yields a well-defined picture of the poles-zeros duality in terms of the freedom to choose between standard and alternative quantization in the strongly coupled sector.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a semi-holographic model for Mott insulators in which a fundamental fermion hybridizes with a composite fermion arising from a large-N holographic strongly interacting sector. Within this setup the Green's function of the composite fermion is stated to exhibit a poles-zeros duality at large N, with the zeros generated by poles of the self-energy that correspond to collective many-body excitations; the duality is explicitly tied to the freedom to choose between standard and alternative quantization in the bulk. The spectral function of the fundamental fermion is then computed to distinguish semi-holographic metallic and Mott-insulating phases.

Significance. If the claimed duality can be shown to arise without fine-tuning and to survive generic deformations of the bulk parameters while remaining interpretable as many-body excitations, the work would supply a concrete holographic mechanism for the poles-zeros structure observed in Mott transitions and would clarify the role of quantization choice in generating that structure. The explicit link between bulk quantization and boundary zeros constitutes a potentially useful technical contribution.

major comments (2)
  1. [Abstract and model-construction section] The central assertion that the composite Green's function 'naturally exhibits' poles-zeros duality at large N (abstract and the model-construction paragraph) rests on the specific choice of quantization; the manuscript does not demonstrate that the zeros persist under generic deformations of the bulk mass or the hybridization coupling while remaining identifiable with collective excitations rather than boundary-condition artifacts.
  2. [Hybridization and spectral-function calculation] The transfer of the duality from the composite to the fundamental fermion via hybridization is load-bearing for the phase characterization; it is not shown that the zeros survive the hybridization without additional tuning or that they continue to correspond to many-body rather than single-particle features after the coupling is turned on.
minor comments (2)
  1. [Notation and definitions] The notation for the self-energy of the composite fermion and its relation to the bulk Dirac solution should be stated explicitly, including the precise definition of the poles that are identified with collective excitations.
  2. [Introduction] A brief comparison with existing holographic treatments of fermionic self-energies (e.g., those employing alternative quantization) would help situate the novelty of the poles-zeros interpretation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive major comments. We address each point below and indicate where revisions will be made to improve clarity and strengthen the claims.

read point-by-point responses

  1. Referee: [Abstract and model-construction section] The central assertion that the composite Green's function 'naturally exhibits' poles-zeros duality at large N (abstract and the model-construction paragraph) rests on the specific choice of quantization; the manuscript does not demonstrate that the zeros persist under generic deformations of the bulk mass or the hybridization coupling while remaining identifiable with collective excitations rather than boundary-condition artifacts.

    Authors: We agree that the poles-zeros duality in the composite Green's function is tied to the choice of quantization (standard versus alternative) in the bulk, as already noted in the abstract. This choice is not an artifact but reflects different physical boundary conditions corresponding to distinct operator dimensions in the dual theory. To address the request for demonstration under generic deformations, we will revise the model-construction section to include a brief analysis showing that the zeros persist for a range of bulk fermion masses near the value considered and remain identifiable with poles of the self-energy arising from the holographic collective modes at large N, rather than purely boundary artifacts. revision: yes

  2. Referee: [Hybridization and spectral-function calculation] The transfer of the duality from the composite to the fundamental fermion via hybridization is load-bearing for the phase characterization; it is not shown that the zeros survive the hybridization without additional tuning or that they continue to correspond to many-body rather than single-particle features after the coupling is turned on.

    Authors: We acknowledge that explicit verification of the duality transfer is necessary to support the phase characterization. In the semi-holographic construction the fundamental fermion acquires a self-energy from the composite sector, so that zeros in the composite Green's function appear as features in the fundamental spectral function. We will revise the hybridization and spectral-function calculation section to add explicit checks confirming that the zeros survive hybridization over the range of couplings examined, without extra tuning, and to clarify that they originate from the large-N collective excitations in the holographic sector (hence many-body in character) rather than single-particle poles. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained in holographic setup.

full rationale

The paper's central claim follows from applying standard holographic techniques—bulk Dirac fermions in AdS with choice between standard and alternative quantization—to generate the composite Green's function and its self-energy poles. These features are then hybridized with the fundamental fermion to produce the observed duality in the spectral function. No step reduces by construction to a fitted parameter renamed as prediction, a self-referential definition, or a load-bearing self-citation whose content is unverified; the quantization freedom is an independent input from AdS/CFT boundary conditions rather than an output derived from the target Mott physics. The derivation therefore remains non-circular and externally falsifiable via the bulk equations of motion.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The proposal rests on the standard large-N holographic duality and the assumption that the composite sector produces the required self-energy structure; no free parameters or new entities are explicitly quantified in the abstract.

axioms (1)
  • domain assumption Large-N limit in the strongly interacting holographic sector produces a Green's function with poles-zeros duality
    Invoked to generate the self-energy for the fundamental fermion.
invented entities (1)
  • hybridized composite fermion no independent evidence
    purpose: To mediate the self-energy that transfers poles-zeros duality to the fundamental fermion
    Introduced as the coupling mechanism between fundamental and holographic sectors.

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