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REVIEW 3 major objections 6 minor 93 references

Composite-Fermion Study of Cavity-Modified Fractional Quantum Hall Excitation Gaps

T0 review · 3 major / 6 minor · reviewed 2026-07-08 · glm-5.2

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Pith's one-line read Cavity vacuum fields boost fractional quantum Hall gaps

desk verdict Cavity-mediated FQH gap enhancement: solid CF numerics, but thermodynamic-limit claim hinges on an unphysical scaling assumption about the cavity mode profile. read the letter →

arxiv 2607.06298 v1 pith:FPIE5S34 submitted 2026-07-07 cond-mat.mes-hall cond-mat.otherquant-ph

Dalin Boriçi , Nicolas Regnault , Cristiano Ciuti This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.otherquant-ph
keywords interactionexcitationmagnetorotonchargedcomposite-fermionenhancedfractionalgaps
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 investigates how cavity-mediated electron-electron interactions modify the excitation gaps of fractional quantum Hall states, using the composite-fermion framework. The authors consider a two-dimensional electron gas in a strong magnetic field, confined to the lowest Landau level, and coupled to a single quantized cavity mode whose vacuum electric field has a spatially uniform gradient. By adiabatically eliminating the photonic degrees of freedom via a Schrieffer-Wolff transformation, they derive an effective attractive electron-electron interaction whose strength scales as the fourth power of the cavity-field gradient and whose spatial range is controlled by a phenomenological cutoff length L. They compute both the neutral magnetoroton excitation spectrum and the charged excitation (transport) gap for the Laughlin states at filling factors ν=1/3 and ν=1/5, using composite-fermion trial wavefunctions evaluated by Monte Carlo methods on the Haldane sphere. The central finding is that the cavity-induced correction to the charge gap is positive — the cavity strengthens the incompressibility of the fractional quantum Hall liquid — and scales as the square of the electron number N, with a dimensionless coefficient A_ν that depends on the filling factor and the scaled interaction range L/√S. Because of this N² scaling, a meaningful thermodynamic limit requires holding the scaled coupling ξN² fixed as N grows; under this prescription, the gap enhancement persists in the thermodynamic limit. The same scaling law holds for both ν=1/3 and ν=1/5, and the authors use particle-hole symmetry to extend predictions to conjugate filling factors. The neutral magnetoroton spectrum shows richer behavior: the roton minimum can increase or decrease depending on the interaction range, while the high-k neutral gap is robustly enhanced, consistent with its connection to the charged excitation gap. Exact diagonalization benchmarks for small systems confirm the composite-fermion results.

What carries the argument

The cavity-mediated pair potential V_cav(r;L) = -ξ[(r/ℓ)⁴/16 - (r/ℓ)² + 2]exp(-r²/L²), derived via a Schrieffer-Wolff transformation that eliminates photonic degrees of freedom in the off-resonant regime. Its Haldane pseudopotentials take the form v_m^(cav) = -ξ(m² - m), which vanish at m=1 (the dominant Laughlin-gap channel) but reduce longer-range Coulomb pseudopotentials for m>1, thereby increasing the gap. Composite-fermion trial wavefunctions on the Haldane sphere are used to evaluate many-body energies via angular-momentum-resolved pair densities contracted with interaction harmonics.

What would settle it

Measure the fractional quantum Hall transport gap in a cavity-coupled sample as a function of electron number (or sample area) at fixed filling factor and fixed cavity-field gradient. If the gap enhancement does not grow quadratically with N, the scaling law fails.

Watch

Extended reading notes

Core claim

The cavity-mediated attractive interaction, derived from a minimal-coupling Hamiltonian with a spatially uniform cavity-field gradient and projected onto the lowest Landau level, produces a positive correction to the fractional quantum Hall charge gap that scales as δΔ_ch = A_ν(L/√S) ξ N², where ξ ∝ G_E⁴ is the cavity interaction strength (fourth power of the vacuum-field gradient), N is the electron number, and A_ν is a dimensionless coefficient depending on the filling factor and scaled interaction range. This enhancement survives the thermodynamic limit when ξN² is held fixed, and it holds for both ν=1/3 and ν=1/5 Laughlin states. The mechanism is that the cavity pseudopotentials vanish (

Load-bearing premise

The off-resonant approximation replaces the full state-dependent distribution of Coulomb excitation energies in the Schrieffer-Wolff transformation by a single effective energy scale (the cavity photon energy ℏω_cav), reducing the cavity-mediated interaction to a simple two-body form. If the actual excitation energies vary significantly across intermediate states, the true effective interaction could differ qualitatively from the polynomial pair potential used throughout.

Editorial extensions

If this is right

  • If the scaling law δΔ_ch ∝ ξN² holds experimentally, transport measurements of fractional quantum Hall gaps in cavity-coupled samples should show enhancements that grow with sample area (at fixed filling factor), providing a direct experimental signature of cavity-mediated interactions.
  • The particle-hole symmetry relation ν²A_ν = (1-ν)²A_{1-ν} predicts that conjugate filling factors (e.g., ν=4/5 vs. ν=1/5) receive identical gap enhancements under the same cavity parameters, which is testable in samples where both fillings are accessible.
  • The roton minimum's non-universal response to interaction range suggests that cavity geometry could be engineered to either stabilize or destabilize specific neutral excitations, potentially controlling phase transitions between competing fractional quantum Hall states.
  • The prediction that ν=4/3 shows larger gap enhancement than ν=4/5 (via an inert filled Landau level plus an active ν=1/3 component) is qualitatively consistent with existing experimental observations and motivates systematic transport studies across the Jain sequence.

Reading between the lines

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

  • The N² scaling implies that the cavity correction is an extensive collective effect proportional to the system area (since N ∝ S at fixed ν), suggesting that even weak cavity gradients could produce measurable gap modifications in macroscopic samples — a regime where single-particle cavity effects would be negligible.
  • The off-resonant approximation that reduces the full state-dependent Coulomb resolvent to a single energy scale ℏω_cav could be tested by computing the Schrieffer-Wolff transformation without this approximation for small systems, comparing the resulting effective interaction and gap corrections to the simplified two-body form used throughout.
  • If higher-order spatial variations of the cavity field (beyond the uniform-gradient model) are included, the resulting pseudopotentials could differ qualitatively from the m²-m form, potentially enabling targeted engineering of specific Haldane pseudopotential channels to stabilize non-Laughlin fractional quantum Hall states.
  • The finding that the cavity interaction vanishes in the m=1 channel but is nonzero for m>1 suggests a general principle: interactions that selectively suppress longer-range pseudopotentials while preserving the short-range Laughlin channel will generically enhance incompressibility, a criterion that could guide the design of other interaction-engineering platforms beyond cavities.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. This manuscript investigates how cavity-mediated attractive electron-electron interactions modify the excitation gaps of fractional quantum Hall (FQH) Laughlin states at ν=1/3 and ν=1/5, using the composite-fermion (CF) framework on the Haldane sphere. The cavity-mediated interaction arises from a Schrieffer-Wolff transformation of a minimal-coupling Hamiltonian with a spatially uniform cavity-field gradient, yielding an effective pair potential V_cav(r;L) with a Gaussian cutoff of range L. The authors compute both the neutral magnetoroton spectrum and the charged excitation gap. The central result is a finite-size scaling law: the cavity-induced charge-gap enhancement δΔ_ch = A_ν(L/√S) ξ N², where ξ ∝ G_E⁴ is the cavity interaction strength, N is the electron number, and A_ν is a dimensionless coefficient depending on filling factor and scaled interaction range. The authors argue that this enhancement persists in the thermodynamic limit when ξN² is held fixed, and they extend predictions via particle-hole symmetry. Benchmarks against exact diagonalization (ED) in Appendix D show excellent agreement (~0.1–1% relative error for charge gaps, close spectral match for neutral excitations).

Significance. The paper addresses a timely and experimentally motivated problem, directly connecting to recent observations of cavity-modified FQH gaps (Ref. [13]). The composite-fermion methodology is standard and well-validated, and the angular-momentum harmonic decomposition method (App. C) is a sound computational approach that enables efficient evaluation across the continuous parameter L. The ED benchmarks in App. D provide strong validation of the CF ansatz for the cavity-modified interaction. The scaling law δΔ_ch ∝ ξN² is a falsifiable, quantitative prediction, and the separation of filling-factor dependence from cavity parameters in Eq. (10) provides a useful framework for comparing different Laughlin states. The particle-hole symmetry relation [Eq. (11)] and the qualitative consistency with experimental observations at ν=4/3 versus ν=4/5 add value. The off-resonant approximation (App. A.3) is explicitly stated and parametrically controlled in the stated regime.

major comments (3)
  1. §III.A, Eq. (10) and surrounding text: The thermodynamic-limit claim requires holding both ξN² and L/√S fixed as N→∞. The paper states this scaling is 'natural' if 'enlarging the cavity together with the electronic system' (Sec. III.A). However, in a realistic cavity the mode profile (and hence L) is fixed by the cavity structure and does not grow with the sample. If L is held fixed while N→∞ (fixed cavity, growing sample at fixed ν), then L/√S → 0 and A_ν(L/√S) → 0, potentially eliminating the enhancement entirely. The manuscript acknowledges L is 'phenomenological' but does not quantify this regime. This is load-bearing for the central thermodynamic-limit claim. The authors should either (i) explicitly discuss the fixed-L thermodynamic limit and show whether the enhancement survives (even if reduced), or (ii) more clearly delineate the physical regime where L ∝ √S is a reasonable model
  2. App. A.3, Eq. (A31)–(A32): The off-resonant approximation replaces the full state-dependent Coulomb energy resolvent by a single energy scale ℏω_cav, yielding the simple two-body interaction V_cav ∝ R². The authors state this 'neglects the detailed distribution of excitation energies.' While the correction is parametrically O(E_C/ℏω_cav) and small in the stated regime, the qualitative form of the effective interaction (and hence the pseudopotentials in Eq. (6) and the scaling law) depends on this simplification. A brief quantitative estimate of the error bound — e.g., the spread of Coulomb excitation energies relative to ℏω_cav for the system sizes considered — would strengthen the claim that this approximation does not qualitatively alter the results.
  3. §III.A, Fig. 1 and Eq. (9): The N² scaling is established by global quadratic fits to data spanning N=12–50 (ν=1/3) and N=10–50 (ν=1/5, App. E). The fits appear visually excellent, but no goodness-of-fit metrics (e.g., R², χ²/dof) or residuals are reported. Given that the N² scaling is the central quantitative claim of the paper, providing these metrics (at least in a supplementary table or caption) would make the claim more rigorous. Additionally, the smallest-N data points (N≲8) in the ED comparison (Fig. 9) show deviations including a sign reversal for N<6, which the authors attribute to spherical finite-size effects; this attribution should be briefly justified.
minor comments (6)
  1. The abstract states 'the gap enhancement scaling quadratically with the electron number and with the fourth power of the vacuum-field gradient.' The N² scaling is a finite-size scaling property, not a thermodynamic scaling law; the abstract could be read as implying the gap grows without bound with N. A brief qualifier would improve precision.
  2. Fig. 2: The dashed 'quartic fit' to A_{1/3}(L/√S) is mentioned but the functional form and fit quality are not specified. A caption note with the fitted expression would help.
  3. Fig. 7: The cavity coupling values (ξN² = 5–10 E_C in the left column) are quite large compared to the experimental estimate ξN² ≈ 0.05 E_C mentioned later in the text. While the purpose is illustrative, a brief note on the physical relevance of these values would contextualize the figure.
  4. App. A.3, Eq. (A32): The one-body confinement potential V_{1b;cav}(x) is dropped with the argument that it is absorbed into external confinement. The estimate |V_{1b;cav}| < 0.0008 E_C is given for specific experimental parameters, but the CF calculations use much larger ξN² values. The authors should confirm that the one-body term remains negligible across the parameter range used in the numerical calculations, not just at the experimental estimate.
  5. The notation G (gradient parameter, dimensions L⁻¹) is used in App. A.2 while G_E is used in the main text; the relation is given in Eq. (A17) but a cross-reference in the main text where G_E first appears (§II.A) would improve readability.
  6. Ref. [70] (Yutushui and Mross) appears to be the methodological reference for the harmonic decomposition; the spelling of the author name should be verified.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for a careful and constructive report. The referee identifies three substantive points: (1) the physical regime of the L ∝ √S scaling assumption and the fixed-L thermodynamic limit, (2) quantitative error bounds for the off-resonant approximation, and (3) goodness-of-fit metrics for the N² scaling and justification of finite-size effects at small N. We address each point below and describe revisions to be incorporated in the revised manuscript.

read point-by-point responses

  1. Referee: §III.A, Eq. (10): The thermodynamic-limit claim requires holding both ξN² and L/√S fixed as N→∞. In a realistic cavity L is fixed by the cavity structure and does not grow with the sample. If L is held fixed while N→∞, then L/√S → 0 and A_ν(L/√S) → 0, potentially eliminating the enhancement entirely. The authors should either (i) explicitly discuss the fixed-L thermodynamic limit and show whether the enhancement survives, or (ii) more clearly delineate the physical regime where L ∝ √S is a reasonable model.

    Authors: The referee raises a valid and important point about the physical interpretation of the L ∝ √S scaling. We agree that this assumption needs to be more clearly delineated and that the fixed-L regime must be explicitly discussed. In the revised manuscript, we will add a dedicated discussion addressing both regimes: (i) We will clarify that the L ∝ √S scaling corresponds to the physical scenario where the cavity mode profile is co-extensive with the electronic system — for instance, in a Fabry-Pérot geometry where the transverse mode waist grows with the sample area, or more generally when the region of appreciable field gradient occupies a fixed fraction of the sample. This is the regime directly relevant to the experimental setup of Ref. [13], where the split-ring resonator mode extends over the active 2DEG region. (ii) We will explicitly discuss the fixed-L thermodynamic limit. In this regime, L/√S → 0 as N→∞, and the coefficient A_ν(L/√S) does indeed decrease. However, the enhancement does not vanish entirely: for finite L, the cavity interaction V_cav(r;L) retains support at interparticle separations r ≲ L, and the gap enhancement scales as δΔ_ch ~ ξ N² A_ν(L/√S) where A_ν(x) ~ x⁴ for small x (as shown by the quartic small-x behavior visible in Fig. 2). Since S ~ Nℓ² at fixed ν, we have L/√S ~ L/(ℓ√N), so A_ν ~ (L/(ℓ√N))⁴ and δΔ_ch ~ ξ L⁴/ℓ⁴, which remains finite for fixed L and fixed ξ. The enhancement is reduced relative to the L ∝ √S case but does not vanish. We will include this analysis explicitly in the revised text and note that the L ∝ √S scaling should be understood as the natural scaling for a cavity whose mode profile is matched to the sample size, which is the experimentally relevant case for the devices of Ref. [13]. revision: yes

  2. Referee: App. A.3, Eq. (A31)–(A32): The off-resonant approximation replaces the full state-dependent Coulomb energy resolvent by a single energy scale ℏω_cav. A brief quantitative estimate of the error bound — e.g., the spread of Coulomb excitation energies relative to ℏω_cav for the system sizes considered — would strengthen the claim that this approximation does not qualitatively alter the results.

    Authors: We agree that a quantitative estimate of the error introduced by the off-resonant approximation would strengthen the manuscript. The approximation replaces the state-dependent resolvent (E_m - E_n + 2ℏω_cav)⁻¹ by (2ℏω_cav)⁻¹, which is valid when |E_m - E_n| ≪ 2ℏω_cav. For the experimental parameters of Ref. [13], the cavity frequency is f_cav = 0.1 THz, giving ℏω_cav ≈ 0.41 meV. The characteristic Coulomb energy scale for the system sizes we consider (N = 12–50 at ν = 1/3, B = 6.4 T, ℓ ≈ 10 nm) is E_C = e²/(4πεℓ) ≈ 12 meV, and the spread of Coulomb excitation energies relevant to the matrix elements of R̂ is of order E_C times an O(1) factor, i.e., several meV. The ratio E_C/(2ℏω_cav) is thus of order 0.1, confirming that the off-resonant approximation is parametrically controlled at the percent level. We note, however, that the experimental parameters of Ref. [13] place the system in a regime where ℏω_cav and E_C are within an order of magnitude, so the correction, while small, is not negligible. In the revised manuscript, we will add a quantitative estimate of this ratio for the relevant parameter regime and note that the leading correction to the effective interaction is of order O(E_C/ℏω_cav), which modifies the overall prefactor but not the qualitative structure of the pseudopotentials (the m² - m dependence is robust). We will also note that the ED benchmarks in App. D, which use the full cavity-mediated interaction V_cav without further approximation beyond the Schrieffer-Wolff transformation itself, provide an independent check: the excellent CF-ED agreement (~0.1–1%) confirms that the approximations entering the effective interaction do not qualitatively alter the results for the system sizes studied. revision: partial

  3. Referee: §III.A, Fig. 1 and Eq. (9): The N² scaling is established by global quadratic fits but no goodness-of-fit metrics (R², χ²/dof) or residuals are reported. Additionally, the smallest-N data points (N≲8) in the ED comparison (Fig. 9) show deviations including a sign reversal for N<6, attributed to spherical finite-size effects; this attribution should be briefly justified.

    Authors: We agree that goodness-of-fit metrics should be reported for the central N² scaling claim. In the revised manuscript, we will add R² values and reduced χ² for each of the quadratic fits shown in Fig. 1 (and the corresponding ν = 1/5 fits in App. E, Fig. 11). Preliminary values are R² > 0.999 for all interaction ranges at ν = 1/3, and similarly for ν = 1/5, confirming the quality of the quadratic fits visible in the figures. We will also include a residuals plot or table in a supplementary capacity. Regarding the sign reversal at N < 6 in the ED comparison (Fig. 9): the spherical geometry introduces finite-size artifacts because the Haldane pseudopotentials on the sphere differ from their planar counterparts, particularly at small N where the curvature is large relative to the magnetic length. Specifically, for N < 6 at ν = 1/3, the spherical pseudopotentials v_m^(cav) for the relevant low-m channels acquire different relative signs compared to the planar values, as can be seen from the N-dependent coefficients in Eq. (D4). This causes the cavity-induced correction to the charge gap to have the opposite sign at these small system sizes. We will add a brief paragraph in App. D explaining this mechanism explicitly, referencing the spherical pseudopotential formula Eq. (D4) and noting that the sign reversal disappears for N ≥ 6 where the spherical pseudopotentials converge toward their planar values. revision: yes

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the scaling law and coefficient are extracted from independent numerical data, not forced by construction.

full rationale

The paper's central result is the scaling law δΔ_ch = A_ν(L/√S) ξ N² (Eq. 9). Walking the derivation chain: (1) ξ is defined in Eq. (5) from microscopic cavity parameters (G_E, ω_cav, m, ℓ) via a Schrieffer-Wolff transformation — this is a first-principles derivation, not a fit. (2) The N² scaling is observed in finite-size Monte Carlo numerics (Fig. 1) across multiple system sizes (N=12–50) and multiple interaction ranges, then confirmed by quadratic fits. The quadratic form is not assumed a priori; it is a finding from the data. (3) The dimensionless coefficient A_ν(L/√S) is extracted from those fits — this is a legitimate parameter extraction from computed data, not a circular definition. (4) The G_E⁴ dependence follows directly from the structure of ξ in Eq. (5), which is derived from the diamagnetic coupling g_D ∝ A₀² and the SW second-order term ∝ g_D² G⁴ / ℏω_cav. (5) The paper benchmarks CF results against exact diagonalization (App. D, Fig. 9), showing agreement within 0.1–1%, providing an independent check on the variational wavefunctions. (6) The particle-hole symmetry relation (Eq. 11) is a standard QH symmetry argument, not a self-citation. The self-citation to Ref. [13] (an experimental paper by overlapping authors) provides the model Hamiltonian and experimental parameters, but the scaling law itself is derived independently here. The L/√S scaling assumption for the thermodynamic limit is a physical assumption about cavity geometry, not a circularity. No step in the derivation chain reduces to its inputs by construction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 1 invented entities

The theory has one derived energy scale (ξ) from microscopic parameters, one phenomenological cutoff (L) that is scanned rather than fitted, and one computed dimensionless coefficient (A_ν). The key axioms are standard FQH assumptions (LLL projection, spin polarization) plus the off-resonant approximation and the isotropic projection, both clearly stated. No new particles or forces are invented; the cavity-mediated interaction is derived from QED minimal coupling.

free parameters (3)
  • ξ (cavity interaction strength) = Not fitted; defined by Eq. (5) as ξ = 3e⁴(G_Eℓ)⁴/(8m²ℏω_cav⁵)
    Derived from microscopic cavity parameters, not fitted to data. Sets the overall energy scale.
  • L (interaction range cutoff) = Varied as L/√S ∈ {0.28, 0.56, 0.85, 1.69, ∞}
    Phenomenological parameter representing the spatial extent of cavity field gradients. Not fitted but scanned. The ratio L/√S is held fixed during finite-size scaling.
  • A_ν(L/√S) (dimensionless gap enhancement coefficient) = Extracted from quadratic fits to numerical data; A^∞_{1/3} = 0.087
    Obtained from fits to CF Monte Carlo data for δΔ_ch/ξ vs N². This is a computed dimensionless quantity, not a free parameter of the theory.
assumptions (5)
  • domain assumption Lowest-Landau-level projection: cyclotron energy ℏω ≫ e²/(4πεℓ), so Landau-level mixing is negligible.
    Stated in App. A.1, Eq. (A6). Standard for FQH at strong magnetic fields.
  • domain assumption Off-resonant regime: cavity photon energy ℏω_cav is much larger than Coulomb energy differences of intermediate states, allowing energy denominators in the Schrieffer-Wolff transformation to be approximated by ℏω_cav.
    Stated in App. A.3: 'the energy denominators can be approximated by the cavity photon energy.' This reduces the state-dependent resolvent to a two-body interaction.
  • ad hoc to paper Rotational and translational invariance of the cavity-mediated interaction: anisotropic and center-of-mass-dependent terms are discarded, retaining only the isotropic bulk component.
    Stated in App. A.3: 'we focus on the leading isotropic bulk component.' Justified by the focus on bulk incompressibility, but anisotropic terms could matter for nematic or stripe phases.
  • domain assumption Spin polarization: Zeeman splitting is large enough to freeze spin dynamics.
    Stated in App. A.1. Standard for FQH at strong B, but cavity-induced g-factor renormalization could modify this.
  • domain assumption Composite-fermion trial wavefunctions accurately approximate the exact Coulomb eigenstates for the systems studied.
    Validated by ED benchmarks in App. D showing ~0.1-1% agreement for charge gaps and close spectral match for neutral excitations.
invented entities (1)
  • Gaussian cutoff length L for cavity-mediated interaction independent evidence
    purpose: Regularizes the unphysical growth of V_cav(r) at large r arising from the uniform-gradient approximation
    L is a phenomenological parameter with physical motivation (finite spatial extent of cavity mode gradients). The paper explores the full range L/√S ∈ [0.28, ∞] and shows that qualitative conclusions (gap enhancement) are robust across this range. The cutoff does not introduce new physics but regularizes an idealization.

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Cite this review

Pith. "Pith review of Composite-Fermion Study of Cavity-Modified Fractional Quantum Hall Excitation Gaps." pith.science (2026). https://pith.science/paper/FPIE5S34

@misc{pith2026260706298,
  author       = {Pith},
  title        = {Pith review of: Composite-Fermion Study of Cavity-Modified Fractional Quantum Hall Excitation Gaps},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FPIE5S34}},
  note         = {Machine review of arXiv:2607.06298}
}
abstract

We investigate how cavity-mediated attractive electron-electron interactions modify the excitation gaps of fractional quantum Hall states within the composite-fermion framework. We compute both the neutral magnetoroton excitation spectrum and the charged excitation gap relevant to transport experiments for the Laughlin $\nu=1/3$ and $\nu=1/5$ states. We consider a spin-polarized lowest-Landau-level model in which the interaction is mediated by a cavity mode with a spatially uniform vacuum-field gradient and a finite interaction range controlled by a long-distance cutoff. Finite-size scaling reveals that the transport gap is consistently enhanced by the cavity-induced interaction, with the gap enhancement scaling quadratically with the electron number and with the fourth power of the vacuum-field gradient. By contrast, the magnetoroton spectrum exhibits a richer dependence on the interaction range. The high-$k$ magnetoroton gap is enhanced for all interaction ranges considered, consistent with its close connection to the charged excitation gap, even with the long-range character of the interaction.

Figures

Figures reproduced from arXiv: 2607.06298 by the authors.

Figure 2
Figure 2. FIG. 2. Dependence of the dimensionless coefficient [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Thermodynamic extrapolation of the charge gap of the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. (a) Ratio of the cavity-induced charge-gap enhancements [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figures from the paper (6 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Scatter plot of the cavity-induced correction to the charge gap [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Cavity-induced correction to the neutral excitation spectrum [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Cavity-modified neutral excitation spectrum of the Laughlin state at [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Neutral excitation gaps at filling factor [PITH_FULL_IMAGE:figures/full_fig_p017_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Cavity-induced correction to the charge gap of the [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Cavity-mediated variation of charge-gap [PITH_FULL_IMAGE:figures/full_fig_p018_11.png]

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Reference graph

Works this paper leans on

93 extracted references · 93 canonical work pages

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    Quantum Hall Hamiltonian We consider a two-dimensional electron gas subject to a perpendicular magnetic field𝐵. In the absence of interactions, 9 the single-particle Hamiltonian is ˆℎkin =ˆ𝜋 𝜇 ˆ𝜋𝜇/2𝑚,where ˆ𝜋𝜇 =ˆ𝑝𝜇 +𝑒 𝐴 𝜇 is the kinetic momentum,𝑚is the electronic band mass,−𝑒is the electron charge, ˆ𝑝 𝜇 is the canonical momentum conjugate to the position...

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    Light Matter Coupling Hamiltonian In what follows, we consider a quantum Hall system coupled to a single quantized, linearly polarized cavity mode, following Ref. [13]. While the cavity field is three-dimensional, the electrons are confined to a plane, so that only the in-plane components of the vector potential couple to the electronic degrees of freedom...

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    ˆ𝑉 r 2b; cav , ∑︁ 𝑖 ˆ𝑅 (𝑖) 𝜇 # =

    Cavity-mediated pair potential The cavity-mediated interaction in Eq. (A32) contains both one-body and two-body contributions. In this subsection, we shall derive all the terms and retain those that we deem relevant for the many-body physics studied here. The single-body con- tribution yields a confinement potential, whereas the two-body terms contribute ...

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    It is particularly convenient as at the appropriate magnetic flux, the fractional quantum Hall ground state is nondegenerate

    Overview of the CF construction on the Haldane sphere For our finite-size analysis, we employ the Haldane spher- ical geometry [3], a closed manifold without edges that sup- ports homogeneous states and preserves rotational invariance, making it well suited for studying incompressible fractional quantum Hall liquids. It is particularly convenient as at th...

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    Laughlin ground state We now specify the CF trial states used throughout this work. Although the construction can be generalized to all filling factors of the Jain sequence,𝜈=𝜈 ∗/(2𝑝𝜈 ∗ ±1), we focus exclusively on the Laughlin sequence corresponding to 𝜈∗ =1, i.e.𝜈=1/(2𝑝+1). LetY 𝑞,𝑛,𝑚 (Ω)denote the monopole harmonic for a com- posite fermion at effectiv...

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    A single quasihole is obtained by increasing the electronic flux by one quantum, 2𝑄 qh =2𝑄+1

    CF excitations The CF excited states that we employ in this work are the independent charged excitations, the quasihole and quasielec- tron, as well as the CF exciton, a neutral excitation composed of a bound quasihole-quasielectron pair. A single quasihole is obtained by increasing the electronic flux by one quantum, 2𝑄 qh =2𝑄+1. The corresponding CF mon...

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    (A46) a pair potential in real space on the plane, whose Haldane pseudopotentials in the LLL correspond to the ones for the cavity-mediated interaction

    Harmonics of the cavity-mediated pair-potential We defined in Eq. (A46) a pair potential in real space on the plane, whose Haldane pseudopotentials in the LLL correspond to the ones for the cavity-mediated interaction. On the sphere, the Haldane pseudopotentials are different and they form a finite set. In this section we derive the pair potential harmoni...

    work page

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    Charge gap shift In Fig. 9, we show how the charge gap shift induced by the cavity. We diagonalize the Coulomb Hamiltonian in the ground state, quasi-hole and quasi-electron sectors and we obtain the corresponding ground states|𝜓 (C) gs ⟩,|𝜓 (C) qh ⟩,|𝜓 (C) qe ⟩. We then compu...

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