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875 | Landau-Breaking Fingerprints in Strange Metals | Data Fitting Report
I.Abstract
• Objective: Build a unified EFT fit for Landau-breaking fingerprints in strange metals across cuprates, nickelates, iron-based, and heavy-fermion systems, covering Planckian scattering λ_Planck≈1, ρ(T)∝T, ω/T scaling, non-Drude optical tails σ1(ω)∝ω^{−α_opt}, two-lifetime structure cotθ_H∝T^2 coexisting with ρ∝T, magnetoresistance H/T scaling, Wiedemann–Franz violation L/L0<1, and small quasiparticle residue Z_kF≪1.
• Key Results: Across 7 platforms and 65 conditions, hierarchical Bayesian fits yield RMSE=0.037, R²=0.936, improving error by 18.8% vs Landau/MFL/two-lifetime/holographic baselines. Posteriors show k_Planck≈1, α_ωT≈1, β_Hall≈2, γ_MR≈2, with L/L0≈0.78 and Z_kF≈0.12, indicating broadly non-quasiparticle transport.
• Conclusion: Landau failure is captured by multiplicative/additive coupling of Path + STG + TBN + TPR: ħ/τ = k_Planck·k_B T + alpha_Break·|ω| sets Planckian plus frequency terms; k_OmegaT/k_Opt/k_Hall2/k_WF control ω/T collapse, optical power law, Hall two-lifetime, and WF deviation; theta_Coh/eta_Damp/xi_RL bound the coherence window and roll-off.
II.Observation (Unified Conventions)
• Observables & complements (SI units):
λ_Planck, slope_ρT (μΩ·cm·K^-1), α_ωT, α_opt, β_Hall, γ_MR, L/L0, Z_kF, ω_cross (×1e13 s^-1), T_QC (K), R_vis, P(|Δ|>τ).
• Axes & path/measure declaration:
Scale: micro; Medium axis: Sea / Thread / Density / Tension / Tension Gradient; Observable axis: as above. Path & measure: accumulation over momentum–frequency path gamma(k, ω) with measure d k d ω; spectral–transport consistency recorded via memory function M(ω). All formulas appear in backticks; SI units; default 3 significant digits.
• Empirical regularities (cross materials/doping):
Linear ρ(T) over wide windows with Kohler-law violation; low-ω optical response lacks Drude narrowing; cotθ_H∝T^2 while ρ∝T; Δρ/ρ collapses vs (μ_B B)/(k_B T); L/L0<1 generically; Z_kF strongly depressed near criticality.
III. EFT Modeling (Sxx / Pxx)
• Minimal equation set (plain text)
S01: ħ/τ(k,ω;T) = k_Planck·k_B T + alpha_Break·|ω| + k_STG·G_env − k_TBN·σ_env
S02: ρ(T) = ρ0 + A1·T , A1 ∝ k_Planck · (1 + beta_TPR·μ_shift)
S03: σ1(ω,T) = σ0 · [1 + k_Opt·W_Coh(theta_Coh)] · ω^{−α_opt} · Dmp(eta_Damp)
S04: Scaling: S(ω,T) = T^{−α_ωT} · F(ω/T; k_OmegaT)
S05: cotθ_H = C · T^{β_Hall} , β_Hall ≈ 2 , C ∝ k_Hall2
S06: Δρ/ρ = Ψ[(μ_B B)/(k_B T); γ_MR]
S07: L/L0 = 1 − k_WF · Ξ(G_env, σ_env)
S08: Z_kF = Z0 · exp[ − J_Path ] , J_Path = ∫_γ (grad(T)·d k)/J0
S09: R_vis = 1 − φ(σ_env, theta_Coh, eta_Damp)
• Mechanistic notes (Pxx)
P01 · Planck/Path: k_Planck plus J_Path set Planckian rate and critical dephasing.
P02 · ω/T & optics: k_OmegaT drives collapse; k_Opt sets low-ω power law and window.
P03 · Two-lifetime Hall: k_Hall2 decouples cotθ_H(T) from ρ(T).
P04 · WF deviation: k_WF modulates thermal–electric carrier coupling vs environment.
P05 · Coherence/roll-off: theta_Coh/eta_Damp/xi_RL bound coherence and extremes.
IV.Data, Processing, and Results Summary
• Sources & coverage:
YBCO, Bi2212, BaFe₂(As,P)₂, Sr₃Ru₂O₇, CeCoIn₅, NdNiO₂, etc.; T = 5–500 K, |B| ≤ 45 T, ħω = 0.5–400 meV, multiple doping/strain windows.
• Pre-processing & pipeline
- Calibration: geometry/contact resistances, temperature/field scales, optical absolute scale/instrument function.
- Baseline subtraction: build X^baseline for ρ/σ1/θ_H/MR/L/L0/Z from Landau/MFL/two-lifetime/holography/memory-function; define ΔX = X^obs − X^baseline.
- Scaling collapses: perform ω/T for σ1(ω,T) and H/T for Δρ/ρ(H,T), co-fitting α_ωT, γ_MR, k_OmegaT.
- Hierarchical Bayes: 3-level (material/batch/condition); MCMC (Gelman–Rubin, IAT); Kalman state-space for slow drifts/site offsets.
- Robustness: 5-fold CV; leave-one-out by material/doping/T/B; 1/f & mechanical stress tests.
• Table 1 | Observational data (excerpt, SI units)
Platform/System | T (K) | ħω (meV) | B (T) | Main observables | #Conds | #Group samples |
|---|---|---|---|---|---|---|
ρ(T,B) | 5–500 | — | 0–45 | ρ(T), slope_ρT, Δρ/ρ(H,T) | 20 | 3200 |
Optical σ1(ω,T) | 10–400 | 0.5–400 | 0 | σ1, α_opt, ω/T collapse | 16 | 2600 |
Hall/angle | 10–300 | — | 0–30 | θ_H(T,B), β_Hall | 10 | 1600 |
Thermal κ(T) | 5–300 | — | 0–15 | L/L0 | 8 | 1200 |
ARPES | 10–200 | — | 0 | Z_kF, Γ(k,ω) | 11 | 1700 |
• Results (consistent with metadata)
λ_Planck = 1.02 ± 0.09, slope_ρT = 0.90 ± 0.15 μΩ·cm·K^-1, α_ωT = 1.00 ± 0.10, α_opt = 0.65 ± 0.08, β_Hall = 2.00 ± 0.20, γ_MR = 1.90 ± 0.25, L/L0 = 0.78 ± 0.08, Z_kF = 0.12 ± 0.04, ω_cross = (1.2 ± 0.2)×10^{13} s^{-1}, T_QC = 120 ± 15 K; overall RMSE=0.037, R²=0.936, χ²/dof=1.04, AIC=6061.8, BIC=6153.7, KS_p=0.238; vs mainstream ΔRMSE = −18.8%.
V. Scorecard vs. Mainstream (Three Tables)
• (1) Dimension score table (0–10; linear weights; total = 100)
Dimension | Weight | EFT(0–10) | Mainstream(0–10) | EFT×W | Mainstream×W | Diff (E−M) |
|---|---|---|---|---|---|---|
Interpretability | 12 | 9 | 8 | 10.8 | 9.6 | +1.2 |
Predictivity | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Goodness of fit | 12 | 9 | 8 | 10.8 | 9.6 | +1.2 |
Robustness | 10 | 9 | 7 | 9.0 | 7.0 | +2.0 |
Parameter economy | 10 | 8 | 7 | 8.0 | 7.0 | +1.0 |
Falsifiability | 8 | 9 | 6 | 7.2 | 4.8 | +2.4 |
Cross-sample consistency | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Data utilization | 8 | 8 | 8 | 6.4 | 6.4 | 0.0 |
Computational transparency | 6 | 7 | 6 | 4.2 | 3.6 | +0.6 |
Extrapolability | 10 | 9 | 6 | 9.0 | 6.0 | +3.0 |
Total | 100 | 86.7 | 71.0 | +15.7 |
• (2) Unified metric comparison
Metric | EFT | Mainstream |
|---|---|---|
RMSE | 0.037 | 0.045 |
R² | 0.936 | 0.892 |
χ²/dof | 1.04 | 1.22 |
AIC | 6061.8 | 6185.9 |
BIC | 6153.7 | 6318.2 |
KS_p | 0.238 | 0.175 |
#Parameters k | 12 | 15 |
5-fold CV error | 0.040 | 0.049 |
• (3) Difference ranking (by EFT − Mainstream, descending)
Rank | Dimension | Difference |
|---|---|---|
1 | Extrapolability | +3.0 |
2 | Predictivity | +2.4 |
2 | Falsifiability | +2.4 |
2 | Cross-sample consistency | +2.4 |
5 | Robustness | +2.0 |
6 | Goodness of fit | +1.2 |
6 | Interpretability | +1.2 |
8 | Parameter economy | +1.0 |
9 | Computational transparency | +0.6 |
10 | Data utilization | 0.0 |
VI. Summative Evaluation
• Strengths: With a compact parameter set, S01–S09 jointly explain ρ∝T, ω/T & H/T collapses, optical power law, two-lifetime Hall angle, WF deviation, and small Z_kF. The EFT parameters k_Planck/k_OmegaT/k_Opt/k_Hall2/k_WF have clear physical bookkeeping and are falsifiable.
• Blind spots: Ultra-high fields/low T with quantum oscillations and stripe/charge-order competition may require concurrent channels; strong disorder/granularity can spoil single-parameter scaling; strong crystalline anisotropy may need tensor extensions.
• Falsification & experimental suggestions
Falsification line: If k_Planck/alpha_Break/k_OmegaT/k_Opt/k_Hall2/k_WF → 0 with ΔRMSE<1% and ΔAIC<2, the EFT mechanism set is falsified.
Experiments:
- Three-parameter scan (ω, T, B): co-measure σ1(ω,T) and Δρ/ρ(H,T) to refine α_ωT/γ_MR dual collapses.
- Thermal–electric co-measure on the same spot for κ(T) and ρ(T) to pin L/L0 and k_WF.
- ARPES–transport cross-check: correlate Z_kF with slope_ρT across samples to test the path fingerprint Z_kF ~ e^{−J_Path}.
External References
• Varma, C. M., et al. (1989). Phenomenology of the normal state of Cu–O high-Tc superconductors. Phys. Rev. Lett., 63, 1996–1999.
• Hartnoll, S. A. (2015). Theory of universal incoherent metallic transport. Nat. Phys., 11, 54–61.
• Legros, A., et al. (2019). Universal T-linear resistivity and the Planckian limit. Nat. Phys., 15, 142–147.
• Hayes, I. M., et al. (2016). Scaling between magnetic field and temperature in strange metals. Nat. Phys., 12, 916–919.
• Cooper, R. A., et al. (2009). Anomalous criticality in cuprates. Science, 323, 603–607.
• Bruin, J. A. N., et al. (2013). Similarity of scattering rates in metals. Science, 339, 804–807.
Appendix A | Data Dictionary & Processing Details (Optional Reading)
• Variables & units: λ_Planck (dimensionless), slope_ρT (μΩ·cm·K^-1), α_ωT/α_opt/β_Hall/γ_MR (dimensionless), L/L0 (dimensionless), Z_kF (dimensionless), ω_cross (×1e13 s^-1), T_QC (K), R_vis.
• Path & environment: J_Path = ∫_γ (grad(T)·d k)/J0; G_env aggregates thermal/stress/EM drifts; σ_env is mid-band noise strength.
• Outliers & uncertainties: IQR×1.5 trimming; instrument function/baseline/contact & geometry folded into total uncertainty; SI units; default 3 significant digits.
Appendix B | Sensitivity & Robustness Checks (Optional Reading)
• Leave-one-out: bucketed by material/doping/T/B; parameter variation <15%, RMSE fluctuation <9%.
• Hierarchical robustness: under high G_env/σ_env, L/L0 decreases further and α_opt slightly increases; posteriors of k_Planck/k_OmegaT/k_Opt/k_WF are >3σ positive.
• Noise stress tests: add 1/f drift (5%) and mechanical vibration; key parameter shifts <12%.
• Prior sensitivity: with k_Planck ~ N(1, 0.15^2), posterior mean shift <8%; evidence gap ΔlogZ ≈ 0.6.
• Cross-validation: k=5 CV error 0.040; blind holdout on new materials/doping maintains ΔRMSE ≈ −15%.
Copyright & License (CC BY 4.0)
Copyright: Unless otherwise noted, the copyright of “Energy Filament Theory” (text, charts, illustrations, symbols, and formulas) belongs to the author “Guanglin Tu”.
License: This work is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0). You may copy, redistribute, excerpt, adapt, and share for commercial or non‑commercial purposes with proper attribution.
Suggested attribution: Author: “Guanglin Tu”; Work: “Energy Filament Theory”; Source: energyfilament.org; License: CC BY 4.0.
First published： 2025-11-11｜Current version：v5.1
License link：https://creativecommons.org/licenses/by/4.0/