{"id":"a109e58b-8744-4d5a-973c-93644a6baf03","arxiv_id":"2607.06298","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":3,"one_line_summary":"Cavity-mediated attractive interactions enhance the fractional quantum Hall transport gap with a quadratic electron-number scaling and a fourth-power dependence on the vacuum-field gradient, as shown by composite-fermion calculations.","lead":"This paper computes how cavity-mediated attractive electron-electron interactions modify fractional quantum Hall excitation gaps using composite-fermion trial wavefunctions. It finds the transport gap is enhanced, scaling quadratically with electron number and with the fourth power of the cavity field gradient, with the enhancement persisting in the thermodynamic limit.","discovery_kind":"unclear","skeptic_critique":{"model":"glm-5.2","headline":"The N² scaling and thermodynamic-limit claim depend on scaling L with system size, which may be physically unjustified for realistic cavities where the mode profile is fixed.","rationale":"The reader correctly identified the off-resonant approximation as a weak point, and it is a genuine assumption. However, I consider it less load-bearing than the L/√S scaling issue because: (1) the off-resonant approximation is parametrically controlled — the error is O(E_C/ℏω_cav), and the paper operates in a regime where this is small — whereas the L-scaling issue determines whether the central result applies to any realistic experiment; (2) the off-resonant approximation affects the form of the interaction but not the scaling law, while the L-scaling directly determines whether the thermodynamic-limit claim holds; (3) the paper itself flags the off-resonant approximation honestly, but treats the L ∝ √S scaling as natural rather than as a strong physical assumption. The ED benchmarks (App. D) validate the CF ansatz and the perturbative treatment of V_cav, which is solid independent support. The N² scaling itself is well-established numerically and the CF-ED agreement is excellent. The concern is specifically about whether the thermodynamic extrapolation in Fig. 3 corresponds to a physically realizable scenario. The verdict remains CONDITIONAL: the scaling law is internally consistent and numerically validated within its framework, but the physical realizability of the L ∝ √S assumption is unaddressed and potentially critical for connecting to experiments like Ref. [13].","tokens_in":34813,"tokens_out":855,"duration_ms":465336,"concrete_test":"Repeat the finite-size scaling analysis at fixed L (in units of ℓ, not √S) rather than fixed L/√S, for several physical values of L/ℓ corresponding to realistic cavity mode profiles (e.g., L/ℓ ~ 10–50). If δΔ_ch/ξ still grows with N but the coefficient A_ν effectively decreases as L/√S → 0, the thermodynamic enhancement claim weakens for fixed-geometry cavities. If the enhancement saturates or vanishes, the scaling law Eq. (10) does not apply to realistic cavities without also scaling the cavity mode.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim that δΔ_ch = A_ν(L/√S) ξ N² persists in the thermodynamic limit requires holding ξN² fixed while taking N→∞. This is internally consistent as a scaling prescription. However, the claim also requires that L/√S remains fixed as N grows, meaning the cavity interaction range L must scale proportionally to the linear system size √S. The paper states this is natural if 'enlarging the cavity together with the electronic system' (Sec. III.A), but this is a strong physical assumption about the cavity geometry, not a derived consequence. In a realistic cavity, the mode profile (and hence the spatial extent of field gradients) is fixed by the cavity structure and does not grow with the sample. If L is held fixed while N→∞ (fixed cavity, growing sample), then L/√S → 0 and the coefficient A_ν(L/√S) → 0, potentially eliminating the enhancement entirely. The paper acknowledges that L is 'phenomenological' and not derived from a realistic mode profile, but the thermodynamic-limit claim in Eq. (10) — which separates filling-factor dependence from cavity parameters and treats S as a free physical parameter — implicitly assumes the scaling L ∝ √S. Whether this scaling is physically realized depends on cavity design details not addressed here. The off-resonant approximation flagged by the reader (App. A.3) is a secondary concern: it introduces an O(E_C/ℏω_cav) correction that is parametrically controlled and small in the stated regime. The L-scaling issue is more fundamental because it determines whether the headline result survives in any realistic experimental geometry.","agreement_with_reader":"partial"},"referee_report":{"model":"glm-5.2","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).","tokens_in":35022,"tokens_out":1672,"duration_ms":321180,"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":[{"comment":"§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","section":null},{"comment":"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.","section":null},{"comment":"§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.","section":null}],"minor_comments":[{"comment":"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.","section":null},{"comment":"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.","section":null},{"comment":"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.","section":null},{"comment":"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.","section":null},{"comment":"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.","section":null},{"comment":"Ref. [70] (Yutushui and Mross) appears to be the methodological reference for the harmonic decomposition; the spelling of the author name should be verified.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The L-scaling issue raised by the skeptic is the most substantive concern, but on reading the paper I find the authors are reasonably transparent that L is phenomenological and that the thermodynamic scaling prescription (ξN² fixed, L/√S fixed) is a modeling choice rather than a derived consequence. The paper does not overclaim: it frames the results as predictions within a minimal model and discusses realistic cavity geometries as a future direction. I therefore judge this as a presentation/clarification issue rather than a load-bearing error, warranting minor revision. The off-resonant approximation concern is secondary and parametrically controlled. The paper is a solid contribution connecting theory to the recent experimental work in Ref. [13], and the ED benchmarks are convincing."},"author_rebuttal":{"model":"glm-5.2","summary":"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.","responses":[{"response":"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_made":"yes","referee_comment":"§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."},{"response":"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_made":"partial","referee_comment":"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."},{"response":"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_made":"yes","referee_comment":"§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."}],"tokens_in":34912,"tokens_out":1694,"duration_ms":190351,"standing_objections":[]},"desk_editor":{"model":"glm-5.2","letter":"The main thing to know: this paper applies composite-fermion trial wavefunctions to compute the cavity-induced correction to the FQH charge gap — something the GMP formalism in Ref. [13] could not access — and finds a clean N² scaling law for the enhancement. The CF methodology is standard and well-validated, and the benchmarks against exact diagonalization in App. D are genuinely strong: ~0.1–1% relative agreement for charge gaps, close spectral match for neutral excitations. The angular-momentum harmonic decomposition (App. C) is a sensible computational strategy that lets them scan continuously in the cutoff L without re-running Monte Carlo each time. The pseudopotential derivation in App. F is clean and the v_m = -ξ(m² - m) result is a nice transparent starting point. The particle-hole symmetry argument extending predictions to conjugate fillings is a useful, correct observation. The qualitative consistency with the experimental trends in Ref. [13] (larger enhancement at ν=4/3 than ν=4/5) is a point in favor. So the computational physics is solid and the paper earns its main quantitative claim within the model it defines. The soft spot is the thermodynamic-limit interpretation. The N² scaling means you need to hold ξN² fixed to extrapolate, which is fine as a scaling prescription. But the coefficient A_ν depends on L/√S, and the paper assumes L scales proportionally to the linear system size — i.e., you enlarge the cavity with the sample. In a realistic cavity the mode profile 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 the enhancement vanishes. The paper is honest that L is phenomenological, but the headline thermodynamic claim in Eq. (10) implicitly requires L ∝ √S, which is a strong physical assumption about cavity geometry, not a derived consequence. This is the central caveat. The off-resonant approximation (App. A.3) replacing the full Coulomb resolvent by a single energy scale is a secondary concern — it is parametrically controlled in the stated regime and the paper is transparent about it. The isotropic projection discarding anisotropic terms is also minor for the bulk-gap question they address. No code or data is shipped, which reduces reproducibility somewhat, though the methods are standard enough that this is not a blocker. This paper is for theorists and experimentalists working on cavity-modified quantum Hall systems. It deserves a serious referee — the numerics are careful, the benchmarks are convincing, and the scaling law is a genuinely new result within its model. The referee should push the authors to clarify the physical conditions under which L ∝ √S holds and to state more prominently that the thermodynamic-limit claim is conditional on that assumption.","headline":"Cavity-mediated FQH gap enhancement: solid CF numerics, but thermodynamic-limit claim hinges on an unphysical scaling assumption about the cavity mode profile.","tokens_in":35826,"tokens_out":665,"would_cite":true,"duration_ms":128323,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"glm-5.2","headline":"Cavity vacuum fields boost fractional quantum Hall gaps","keywords":[],"falsifier":"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.","tokens_in":34813,"feed_emoji":"🔬","tokens_out":1464,"duration_ms":136157,"temperature":0.7,"pith_summary":"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.","feed_headline":"Cavity vacuum fields boost fractional quantum Hall gaps","feed_subtitle":"Attractive cavity-mediated interactions enhance the charge gap of Laughlin states, scaling as the square of electron number and the fourth功率","key_machinery":"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.","core_discovery":"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 (","pith_inferences":["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."],"forward_implications":["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."],"fun_headline_variants":["Cavity interactions enhance fractional quantum Hall transport gaps","Vacuum-field gradient increases fractional quantum Hall charge gaps","Composite fermions show gap enhancement in cavity-coupled FQH states","Cavity-mediated attraction scales up fractional quantum Hall gaps","Long-range cavity fields enhance Laughlin state charge gaps"],"cache_read_input_tokens":0,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Cavity interactions enhance fractional quantum Hall transport gaps","Vacuum-field gradient increases fractional quantum Hall charge gaps","Composite fermions show gap enhancement in cavity-coupled FQH states","Cavity-mediated attraction scales up fractional quantum Hall gaps","Long-range cavity fields enhance Laughlin state charge gaps"]},"model":"glm-5.2","effort":"high","cost_usd":0.0,"raw_usage":{"total_tokens":1053,"prompt_tokens":526,"completion_tokens":527,"prompt_tokens_details":null},"tokens_in":526,"tokens_out":527,"duration_ms":39284,"temperature":1.0,"reasoning_tokens":472,"cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-08T10:27:08.573425+00:00","model_set":{"reader":"glm-5.2"},"falsifier":"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.","supporting_citations":[],"review_version":1}