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arxiv: 2604.13936 · v1 · submitted 2026-04-15 · ❄️ cond-mat.mes-hall · cond-mat.str-el· quant-ph

Topological markers for a one-dimensional fermionic chain coupled to a single-mode cavity

Anna Ritz-Zwilling , Olesia Dmytruk This is my paper

Pith reviewed 2026-05-10 12:21 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.str-elquant-ph
keywords Su-Schrieffer-Heeger chaincavity QEDtopological markerswinding numberResta polarizationhigh-frequency expansioninteracting fermionsedge states
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0 comments X

The pith

Cavity-mediated interactions in an SSH chain produce consistent topological phases detected by winding number, polarization, and edge correlations.

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

The authors couple a Su-Schrieffer-Heeger chain to a single-mode cavity and focus on the off-resonant regime. They derive an effective interacting fermionic Hamiltonian through high-frequency expansion and then apply three markers designed for interacting systems: two-point correlation functions on open chains to detect edge states, a winding number constructed from the single-particle Green's function, and bulk electric polarization via Resta's many-body formula on periodic chains. These markers agree closely on the resulting phase diagram, confirming that cavity effects can be tracked through the effective electronic model. This approach offers an alternative route to cavity-modified topology that avoids direct solution of the full light-matter Hamiltonian.

Core claim

For a finite-size Su-Schrieffer-Heeger chain coupled to a cavity, the effective fermionic Hamiltonian obtained from high-frequency expansion in the off-resonant regime exhibits topological phases whose boundaries are located consistently by the Green's-function winding number and by Resta polarization; the associated edge states are independently verified by the decay behavior of the two-point correlation function between opposite ends of an open chain.

What carries the argument

Three adapted topological markers—edge two-point correlations, Green's-function winding number, and Resta many-body polarization—applied to the cavity-derived effective interacting Hamiltonian.

If this is right

  • Cavity effects on topology can be studied entirely within an interacting fermionic model rather than the complete light-matter system.
  • The three markers remain reliable even after cavity-induced interactions are included.
  • Edge-state signatures survive in the effective description and can be checked via open-boundary correlations.
  • The method supplies an independent check on phase diagrams previously obtained by direct light-matter treatments.

Where Pith is reading between the lines

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

  • The same marker set could be tested on other one-dimensional chains or on two-dimensional lattices coupled to cavities.
  • Finite-size scaling of the correlation length or polarization could reveal how cavity strength influences the robustness of the topological phase.
  • Experimental platforms such as circuit QED or trapped-ion chains might realize the predicted effective interactions and allow direct measurement of the markers.

Load-bearing premise

The high-frequency expansion remains accurate enough in the off-resonant regime to capture all cavity-mediated interactions that affect the topological markers in the finite-size chain.

What would settle it

A numerical diagonalization of the full light-matter Hamiltonian or an experiment that finds the phase boundaries predicted by the effective model to disagree with those obtained from the winding number or polarization calculations.

Figures

Figures reproduced from arXiv: 2604.13936 by Anna Ritz-Zwilling, Olesia Dmytruk.

Figure 1
Figure 1. Figure 1: FIG. 1. SSH chain placed inside a single-mode cavity with [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Comparison of two-point correlation function [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Phase diagram for a cavity embedded SSH chain with periodic boundary conditions as a function of coupling strength [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Phase diagram for a cavity embedded SSH chain [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

We study a Su-Schrieffer-Heeger chain coupled to a single mode photonic cavity. Considering an off-resonant regime we use the high-frequency expansion in order to obtain an effective fermionic Hamiltonian with cavity-mediated interactions. We characterize the effects of the cavity on topology in a finite size chain by studying three different markers adapted for interacting systems: correlation functions between edges in a chain with open boundary conditions, and a winding number based on the single-particle Green's function and bulk electric polarization via the many-body formula by Resta for a chain with periodic boundary conditions. There is excellent agreement between the winding number and polarization approaches to compute the phase diagram, with the presence of the edge states being confirmed through the calculations of the two-point correlation function. Our approach provides an alternative perspective on cavity-modified topological phases through a study of an effective interacting electronic Hamiltonian and complements methods that treat the full light-matter Hamiltonian directly.

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 studies an SSH fermionic chain coupled to a single-mode cavity in the off-resonant regime. A high-frequency expansion is applied to derive an effective interacting fermionic Hamiltonian with cavity-mediated terms. Topology in finite chains is characterized via three markers: edge two-point correlation functions (open boundaries), winding number from the single-particle Green's function, and Resta polarization (periodic boundaries). Excellent agreement is reported between the winding number and polarization for the phase diagram, with edge states confirmed by the correlations. The work positions this effective-model approach as complementary to direct light-matter treatments.

Significance. If the high-frequency expansion is shown to be faithful, the paper supplies a practical route to cavity-modified topology via an effective electronic Hamiltonian, avoiding full photon-space diagonalization. The use of multiple adapted markers (Green's function winding, Resta polarization, and edge correlations) for interacting systems is a constructive contribution and could aid future studies of light-matter topological phases.

major comments (2)
  1. [Section on model and effective Hamiltonian] The derivation of the effective Hamiltonian via high-frequency expansion (Section on model and effective Hamiltonian) is central to all subsequent claims, yet the manuscript provides no benchmark against the full light-matter Hamiltonian with photon truncation. Direct comparison of phase boundaries or correlation functions, even for small N and truncated photon number, is required to confirm that the reported topology reflects the actual cavity-coupled system rather than an internal property of the approximated model.
  2. [Results section and phase-diagram figures] The claim of 'excellent agreement' between winding number and Resta polarization (results section and phase-diagram figures) is load-bearing for the central conclusion but lacks quantitative support such as tabulated critical-point deviations, overlap integrals of phase regions, or error estimates across parameter scans.
minor comments (2)
  1. [Effective Hamiltonian derivation] Notation for the cavity-mediated interaction terms in the effective Hamiltonian should be cross-referenced explicitly to the original light-matter coupling to aid reproducibility.
  2. [Figure captions] Figure captions for the phase diagrams would benefit from explicit statements of the system size N, photon truncation, and the frequency ratio used in the expansion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive review and the positive assessment of the significance of our work. We address each major comment below and will revise the manuscript to incorporate the suggested improvements.

read point-by-point responses

  1. Referee: The derivation of the effective Hamiltonian via high-frequency expansion (Section on model and effective Hamiltonian) is central to all subsequent claims, yet the manuscript provides no benchmark against the full light-matter Hamiltonian with photon truncation. Direct comparison of phase boundaries or correlation functions, even for small N and truncated photon number, is required to confirm that the reported topology reflects the actual cavity-coupled system rather than an internal property of the approximated model.

    Authors: We agree that a direct benchmark would strengthen the validation of the high-frequency expansion. While the off-resonant regime and the expansion are standard, we will add a new appendix in the revised manuscript comparing the effective model to the full light-matter Hamiltonian for small system sizes (N=4 and N=6) with photon truncation up to 3 photons. This will include comparisons of ground-state energies, edge correlation functions, and the location of phase boundaries to confirm that the topology in the effective model faithfully represents the cavity-coupled system. revision: yes

  2. Referee: The claim of 'excellent agreement' between winding number and Resta polarization (results section and phase-diagram figures) is load-bearing for the central conclusion but lacks quantitative support such as tabulated critical-point deviations, overlap integrals of phase regions, or error estimates across parameter scans.

    Authors: We acknowledge that quantitative metrics would make the agreement more rigorous. In the revised manuscript, we will add a table in the results section (or supplementary material) reporting the deviations in critical points (e.g., the cavity coupling strength g at which the topological transition occurs) between the two markers, along with the overlap fraction of the identified topological regions across the scanned parameter space. This will provide explicit error estimates supporting the visual agreement in the phase diagrams. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard approximation and independent markers

full rationale

The derivation applies the high-frequency expansion (a standard external technique) to obtain an effective fermionic Hamiltonian, then evaluates it with three established topological markers (winding number from single-particle Green's function, Resta polarization, and edge correlation functions). These markers are applied independently to the same effective model; their agreement is a cross-check, not a definitional reduction. No self-citations, fitted parameters renamed as predictions, or ansatz smuggling appear in the load-bearing steps. The chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim depends on the validity of the high-frequency expansion in the off-resonant regime and on the assumption that the chosen markers correctly diagnose topology in the resulting interacting fermionic model.

axioms (2)
  • domain assumption High-frequency expansion accurately yields an effective fermionic Hamiltonian with cavity-mediated interactions
    Invoked to obtain the model whose topology is then studied
  • domain assumption The three markers (edge correlations, Green's function winding number, Resta polarization) are valid for interacting systems
    Used to characterize the phase diagram

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  1. Poor man's Majorana bound states in quantum dot based Kitaev chain coupled to a photonic cavity

    cond-mat.mes-hall 2026-04 unverdicted novelty 6.0

    Cavity photons screen attractive or repulsive interactions in a quantum-dot Kitaev chain, allowing the system to reach the sweet spot for poor man's Majorana bound states.

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