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UNIVERSAL PHASE RELAXATION AND SPECTRAL DIMENSION IN QUANTUM CRITICAL SYSTEMS: THE TRUE FRAMEWORK

Michel Febba

Published Jul 22, 2026• 0 citations
Publisher

Abstract

We present a unified theoretical framework, termed TRUE (Théorie Redistributive Universelle Évolutive), to describe the universal regularities observed in quantum critical systems beyond the Fermi liquid paradigm. We introduce a universal invariant \gamma_0 = 0.13648, derived analytically from the Koszul-Fisher curvature constraint on the symplectic manifold of critical phases, without recourse to any empirical fitting. The effective spectral dimension \tau of the dissipation phase space is defined as the invariant trace of the spectral dissipation tensor. We show that the 0\text{D} \to 1\text{D} crossover (unitary Kondo regime) leads to \tau = \sqrt{2}, whose combination with the curvature constraint yields the characteristic equation x^2 - x + \frac{\sqrt{2}}{12} = 0, whose roots are exactly \gamma_0 = 0.13648 and 1 - \gamma_0 = 0.86352. Quantitative validation is performed on five independent classes of materials (strange metals, iron pnictides, magic-angle graphene, Bechgaard salts, InAs nanowires), with deviations below 5% from the predicted invariant. We discuss the validity conditions of the framework, notably the spatial coherence extension condition \xi > 0, and propose a covariant tensor formalism anchored in Koszul-Souriau information geometry.

DOI
10.5281/zenodo.21487309

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When a quantum system couples to a scale-invariant environment, what form must its decoherence take? We prove that the answer is unique: under locality, Lorentz invariance, unitarity, and continuous scale invariance, the effect of any such environment is mathematically equivalent to that of an \emph{unparticle bath} -- a scale-invariant continuum of states -- characterized entirely by the scaling dimension $d_{\mathcal{U}}$ of the coupled operator. This is not a modelling choice but a consequence of conformal symmetry. All decoherence and dissipation exponents are fixed by $d_{\mathcal{U}}$ through exact consistency relations, providing falsifiable predictions independent of microscopic details. We validate the framework using multi-channel transport data from the unitary Fermi gas, where two genuinely independent observables yield a consistent $d_{\mathcal{U}} = 7/4$. We further show that quantum Ising criticality, inflationary cosmology, and high-energy astrophysical neutrinos -- spanning more than 25 orders of magnitude in energy -- are unified as specific realizations of the same structure. A decoherence phase transition at $d_{\mathcal{U}} = 5/2$, where quantum coherence is \emph{protected} rather thandestroyed at long times, is a qualitative prediction inaccessible to any memoryless dynamical description.

hep-phCross-listedarXiv:2604.15445•Apr 20, 2026•0 citations
We present a unified theoretical framework, termed TRUE (Théorie Redistributive Universelle Évolutive), to describe the universal regularities observed in quantum critical systems beyond the Fermi liquid paradigm. We introduce a universal invariant \gamma_0 = 0.13648, derived analytically from the Koszul-Fisher curvature constraint on the symplectic manifold of critical phases, without recourse to any empirical fitting. The effective spectral dimension \tau of the dissipation phase space is defined as the invariant trace of the spectral dissipation tensor. We show that the 0\text{D} \to 1\text{D} crossover (unitary Kondo regime) leads to \tau = \sqrt{2}, whose combination with the curvature constraint yields the characteristic equation x^2 - x + \frac{\sqrt{2}}{12} = 0, whose roots are exactly \gamma_0 = 0.13648 and 1 - \gamma_0 = 0.86352. Quantitative validation is performed on five independent classes of materials (strange metals, iron pnictides, magic-angle graphene, Bechgaard salts, InAs nanowires), with deviations below 5% from the predicted invariant. We discuss the validity conditions of the framework, notably the spatial coherence extension condition \xi > 0, and propose a covariant tensor formalism anchored in Koszul-Souriau information geometry.
We present the consolidated version of the TRUE framework (Théorie Redistributive Universelle Évolutive), which unifies the description of the universal regularities observed in quantum critical systems beyond the Landau Fermi-liquid paradigm. The fundamental invariant γ₀ = 0.13648 is derived analytically from the Koszul–Fisher curvature equation on the information phase space, with no free parameters. We introduce the spectral scaling law R_raw(τ) = τ · γ₀, where τ is the effective spectral dimension of the system, measured by the trace of the spectral dissipation tensor. We demonstrate the physical equivalence between the ratio of critical fields and the ratio of critical energies via the Zeeman energy E = g μ_B B. Validation is performed on six independent material classes, with deviations systematically below 5 %. We propose a rigorous classification of systems into two categories: predictive systems (τ computable a priori) and complex systems (frustrated lattices), where the invariant becomes a topological diagnostic tool. Three blind predictions are formulated for as-yet untested systems.
Nous présentons un cadre théorique unifié, dénommé TRUE (Théorie Redistributive Universelle Évolutive), pour décrire les régularités universelles observées dans les systèmes critiques quantiques hors du paradigme du liquide de Fermi. Nous introduisons un invariant universel \gamma_0 = 0.13648, dérivé analytiquement à partir de la contrainte de courbure de Koszul-Fisher sur la variété symplectique des phases critiques, sans recours à aucun ajustement empirique. La dimension spectrale effective \tau de l'espace des phases de dissipation est définie comme la trace invariante du tenseur de dissipation spectrale. Nous montrons que le crossover 0\text{D} \to 1\text{D} (régime Kondo unitaire) conduit à \tau = \sqrt{2}, dont la combinaison avec la contrainte de courbure produit l'équation caractéristique x^2 - x + \frac{\sqrt{2}}{12} = 0, dont les racines sont exactement \gamma_0 = 0.13648 et 1 - \gamma_0 = 0.86352. La validation quantitative est effectuée sur cinq classes de matériaux indépendantes (métaux étranges, pnictures de fer, graphène à angle magique, sels de Bechgaard, nanofils InAs), avec des écarts inférieurs à 5 % par rapport à l'invariant prédit. Nous discutons les conditions de validité du cadre, notamment la condition d'extension spatiale de cohérence \xi > 0, et proposons un formalisme tensoriel covariant ancré dans la géométrie de l'information de Koszul-Souriau.
To test the predictive power of the TRUE framework (Théorie Redistributive Universelle Évolutive) and its geometric invariant \gamma_0 = 0.13648, we formulate a set of a priori numerical predictions for three quantum critical systems not yet characterized within this formalism: the Planckian viscosity of the ^6\text{Li} Fermi gas in the unitary regime, the transition ratio of the \alpha\text{-RuCl}_3 spin liquid under field, and the critical energy ratio of the metamagnet \text{Sr}_3\text{Ru}_2\text{O}_7. All numerical values are locked with no free parameters and are accompanied by their spectral dimension \tau, providing a direct experimental verification protocol for the community.
We report the discovery of a new class of critical phenomena in open quantum systems that is not governed by divergence of correlation length. In contrast to the standard paradigm, where criticality is identified by ξ → ∞, we demonstrate the existence of regimes characterized by: Δ → 0, Γ > 0, ξ = O(1), where Δ is the partition gap and Γ is the switching rate of optimal decompositions. We show that such systems exhibit a universal modular scaling law: ν(λ) ∼ 1 log λ, derived from the spectral structure of the modular generator K = −log ρ. This scaling defines a new diagnostic observable independent of spatial correlations. We formulate a hard, experimentally testable prediction: Ξ(λ) = ν(λ) · log λ → 1, which provides a falsifiable signature of modular criticality accessible in quantum simulators. The results establish a new notion of criticality rooted in spectral redistribution, commutator dynamics, and information geometry, rather than correlation length. This reveals a previously unrecognized universality class applicable to open quantum systems, non-equilibrium dynamics, and information-theoretic regimes.
Nous présentons la version consolidée du cadre TRUE (Théorie Redistributive Universelle Évolutive), qui unifie la description des régularités universelles observées dans les systèmes critiques quantiques en dehors du paradigme du liquide de Fermi. L'invariant fondamental γ₀ = 0,13648 est dérivé analytiquement de l'équation de courbure de Koszul-Fisher sur l'espace des phases d'information, sans aucun paramètre libre. Nous introduisons la loi d'échelle spectrale R_brut(τ) = τ · γ₀, où τ est la dimension spectrale effective du système, mesurée par la trace du tenseur de dissipation spectrale. Nous démontrons l'équivalence physique entre le rapport de champs critiques et le rapport d'énergies critiques via l'énergie Zeeman E = g μ_B B. La validation est effectuée sur six classes de matériaux indépendants, avec des écarts systématiquement inférieurs à 5 %. Nous proposons une classification rigoureuse des systèmes en deux catégories : les systèmes prédictifs (τ calculable a priori) et les systèmes complexes (réseaux frustrés), où l'invariant devient un outil de diagnostic topologique. Trois prédictions à l'aveugle sont formulées pour des systèmes non encore testés.
When a quantum system couples to a scale-invariant environment, what form must its decoherence take? We prove that the answer is unique: under locality, Lorentz invariance, unitarity, and continuous scale invariance, the effect of any such environment is mathematically equivalent to that of an \emph{unparticle bath} -- a scale-invariant continuum of states -- characterized entirely by the scaling dimension dUd_{\mathcal{U}}dU​ of the coupled operator. This is not a modelling choice but a consequence of conformal symmetry. All decoherence and dissipation exponents are fixed by dUd_{\mathcal{U}}dU​ through exact consistency relations, providing falsifiable predictions independent of microscopic details. We validate the framework using multi-channel transport data from the unitary Fermi gas, where two genuinely independent observables yield a consistent dU=7/4d_{\mathcal{U}} = 7/4dU​=7/4. We further show that quantum Ising criticality, inflationary cosmology, and high-energy astrophysical neutrinos -- spanning more than 25 orders of magnitude in energy -- are unified as specific realizations of the same structure. A decoherence phase transition at dU=5/2d_{\mathcal{U}} = 5/2dU​=5/2, where quantum coherence is \emph{protected} rather thandestroyed at long times, is a qualitative prediction inaccessible to any memoryless dynamical description.