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arxiv: 2602.22626 · v7 · submitted 2026-02-26 · ❄️ cond-mat.str-el · cond-mat.supr-con

Memory-Dominated Quantum Criticality as a Universal Route to High-Temperature Superconductivity

Byung Gyu Chae This is my paper

Pith reviewed 2026-05-15 19:34 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.supr-con
keywords high-temperature superconductivityquantum criticalitymemory-dominated dynamicsrelaxation spectrumtime-scale density of statesstrange metalpairing kernelnon-Markovian response
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The pith

Finite weight at zero relaxation rate in the spectrum of collective modes produces logarithmic enhancement of pairing and a BCS-like superconducting scale set by infrared spectral weight.

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

The paper shows that near quantum criticality the infrared behavior of electrons is controlled by the spectrum of relaxation rates of collective decay modes. From a microscopic fermionic theory it derives a universal spectral representation of the Cooper-channel kernel in terms of the time-scale density of states of those modes. When this density remains finite at vanishing relaxation rate the kernel develops long-time tails decaying as 1/t, which logarithmically enhance the retarded pairing interaction and drive an exponential transition temperature fixed by the infrared weight. The same spectrum produces long-time correlations and non-Markovian dynamics that account for strange-metal behavior in the normal state. A sympathetic reader would see this as a mediator-independent route to high-temperature superconductivity that follows directly from the structure of quantum-critical relaxation.

Core claim

Starting from a microscopic fermionic theory, the Cooper-channel kernel admits a universal spectral representation in terms of the time-scale density of states (TDOS) of collective decay modes, without invoking a specific bosonic mediator. A finite TDOS at vanishing relaxation rate produces a memory-dominated regime characterized by long-time kernels K(t)∼1/t and logarithmic enhancement of the retarded pairing interaction, leading to a BCS-like exponential transition scale set by infrared spectral weight. More generally, infrared-singular spectra generate power-law response and algebraic enhancement of the transition scale. The same relaxation spectrum controls normal-state dynamics, giving

What carries the argument

The time-scale density of states (TDOS) of collective decay modes, which supplies the universal spectral representation for the Cooper-channel kernel and fixes both the pairing interaction and normal-state memory effects.

Load-bearing premise

The Cooper-channel kernel admits a universal spectral representation solely in terms of the TDOS of collective decay modes from a microscopic fermionic theory, without reference to any particular bosonic mediator.

What would settle it

Observation in a quantum-critical material of finite infrared TDOS weight together with either the complete absence of superconductivity or a transition temperature uncorrelated with that weight would falsify the proposed mechanism.

Figures

Figures reproduced from arXiv: 2602.22626 by Byung Gyu Chae.

Figure 1
Figure 1. Figure 1: FIG. 1. Dynamical universality map of correlated quantum matter. Infrared behavior is organized by the spectrum of relaxation [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Infrared renormalization-group flow of the Cooper [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Experimental consequences of memory–dominated [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Dynamical classification determined by the TDOS [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
read the original abstract

Understanding the dynamical origin of high-temperature superconductivity remains a central challenge in strongly correlated quantum matter. Near quantum criticality, diverging correlation times reorganize the infrared dynamics into a scale-free continuum of collective relaxation processes. We show that the infrared behavior of interacting electrons is generically controlled by the relaxation-rate spectrum of the underlying many-body dynamics. Starting from a microscopic fermionic theory, we derive that the Cooper-channel kernel admits a universal spectral representation in terms of the time-scale density of states (TDOS) of collective decay modes, without invoking a specific bosonic mediator. The superconducting instability follows directly from the vanishing of the quadratic kernel via a standard ladder resummation and Thouless criterion, with the pairing interaction determined entirely by the infrared structure of the relaxation spectrum. A finite TDOS at vanishing relaxation rate produces a memory-dominated regime characterized by long-time kernels $K(t)\sim 1/t$ and logarithmic enhancement of the retarded pairing interaction, leading to a BCS-like exponential transition scale set by infrared spectral weight. More generally, infrared-singular spectra generate power-law response and algebraic enhancement of the transition scale. The same relaxation spectrum controls normal-state dynamics, giving rise to long-time correlations, non-Markovian response, and strange-metal behavior. These results identify the spectral organization of relaxation modes as a universal organizing principle of quantum critical matter and establish memory-dominated criticality as a natural mechanism for enhanced pairing.

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

3 major / 2 minor

Summary. The paper claims that near quantum criticality, diverging correlation times reorganize the infrared dynamics of interacting electrons into a scale-free continuum of collective relaxation processes. Starting from a microscopic fermionic theory, the Cooper-channel kernel is derived to admit a universal spectral representation in terms of the time-scale density of states (TDOS) of collective decay modes, without reference to a specific bosonic mediator. A finite TDOS at vanishing relaxation rate produces a memory-dominated regime with long-time kernels K(t)∼1/t, logarithmic enhancement of the retarded pairing interaction, and a BCS-like exponential superconducting transition scale set by the infrared spectral weight. The same relaxation spectrum governs normal-state long-time correlations and strange-metal behavior, positioning memory-dominated criticality as a universal route to high-Tc superconductivity.

Significance. If the central derivation is made rigorous, the result would identify the spectral organization of relaxation modes as a mediator-independent organizing principle for quantum critical matter, directly linking non-Markovian dynamics to enhanced pairing and strange-metal phenomenology. This offers a parameter-light framework that could unify explanations across cuprates, heavy-fermion systems, and other strongly correlated platforms where quantum criticality and high-Tc coexist.

major comments (3)
  1. [§3 (derivation of the spectral representation)] The central claim that the Cooper-channel kernel admits an exact universal spectral representation K(ω) = ∫ ρ(γ)/(ω + iγ) dγ in terms of the TDOS ρ(γ) of collective relaxation rates, derived directly from a general microscopic fermionic theory without invoking a specific bosonic propagator, is asserted but not supplied with an explicit operator-level, diagrammatic, or functional-integral construction. This step is load-bearing for the universality, the mapping to K(t)∼1/t, and the subsequent logarithmic enhancement.
  2. [§4 (superconducting instability and Thouless criterion)] The application of the standard ladder resummation and Thouless criterion to obtain the superconducting instability relies on the infrared structure of the TDOS, yet the manuscript does not demonstrate how the transition scale remains set solely by the infrared spectral weight once the representation is inserted, nor does it address potential regularization or cutoff dependence arising from the microscopic fermionic self-energy.
  3. [§5 (normal-state dynamics)] The assertion that the identical relaxation spectrum controls both the superconducting pairing and the normal-state strange-metal behavior (long-time correlations, non-Markovian response) is stated without quantitative validation against solvable limits or comparison to established models (e.g., SYK or marginal Fermi liquid), leaving the claimed unification untested.
minor comments (2)
  1. The notation for the TDOS ρ(γ) and the kernel K(t) should be introduced with explicit definitions and units upon first appearance to improve readability.
  2. The abstract states K(t)∼1/t and the logarithmic enhancement; these should be cross-referenced to the corresponding numbered equations in the main text.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. The points raised help clarify the presentation of the central derivation and its implications. We address each major comment below and will incorporate revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [§3 (derivation of the spectral representation)] The central claim that the Cooper-channel kernel admits an exact universal spectral representation K(ω) = ∫ ρ(γ)/(ω + iγ) dγ in terms of the TDOS ρ(γ) of collective relaxation rates, derived directly from a general microscopic fermionic theory without invoking a specific bosonic propagator, is asserted but not supplied with an explicit operator-level, diagrammatic, or functional-integral construction. This step is load-bearing for the universality, the mapping to K(t)∼1/t, and the subsequent logarithmic enhancement.

    Authors: We agree that an explicit construction would strengthen the presentation. In the revised manuscript we will expand §3 with a diagrammatic derivation starting from the microscopic fermionic action in the presence of a general quantum-critical bosonic fluctuation. We integrate out the collective modes to obtain the four-fermion vertex in the Cooper channel, express the resulting kernel via the spectral decomposition of the relaxation-rate density of states, and demonstrate that the representation K(ω) = ∫ ρ(γ)/(ω + iγ) dγ holds independently of the specific bosonic propagator. This will make the universality and the emergence of the 1/t long-time kernel fully explicit. revision: yes

  2. Referee: [§4 (superconducting instability and Thouless criterion)] The application of the standard ladder resummation and Thouless criterion to obtain the superconducting instability relies on the infrared structure of the TDOS, yet the manuscript does not demonstrate how the transition scale remains set solely by the infrared spectral weight once the representation is inserted, nor does it address potential regularization or cutoff dependence arising from the microscopic fermionic self-energy.

    Authors: We will add a dedicated subsection in §4 that inserts the spectral representation into the ladder equation and solves the Thouless criterion explicitly. We show that the superconducting scale is determined solely by the infrared weight of ρ(γ) near γ=0, yielding the BCS-like exponential form. We further demonstrate that ultraviolet divergences from the microscopic self-energy are regularized by the same TDOS and cancel in the memory-dominated regime, rendering the transition temperature independent of microscopic cutoffs. This calculation will be included in the revision. revision: yes

  3. Referee: [§5 (normal-state dynamics)] The assertion that the identical relaxation spectrum controls both the superconducting pairing and the normal-state strange-metal behavior (long-time correlations, non-Markovian response) is stated without quantitative validation against solvable limits or comparison to established models (e.g., SYK or marginal Fermi liquid), leaving the claimed unification untested.

    Authors: We acknowledge that quantitative benchmarks would strengthen the unification claim. In the revised manuscript we will add a new subsection in §5 that compares the predicted long-time correlations and relaxation spectrum to the SYK model in the large-N limit and to the marginal Fermi liquid phenomenology. We show that the TDOS extracted from the SYK saddle-point equations reproduces the known 1/t decay of the Green's function and the linear-in-T resistivity, thereby providing the requested validation within solvable limits. revision: partial

Circularity Check

1 steps flagged

TDOS infrared weight sets BCS scale by construction from normal-state input

specific steps
  1. fitted input called prediction [Abstract]
    "A finite TDOS at vanishing relaxation rate produces a memory-dominated regime characterized by long-time kernels K(t)∼1/t and logarithmic enhancement of the retarded pairing interaction, leading to a BCS-like exponential transition scale set by infrared spectral weight."

    The exponential transition scale is explicitly set by the infrared spectral weight of the TDOS; because the TDOS itself is extracted from or fitted to the normal-state relaxation spectrum (the same input that defines the memory kernels), the superconducting instability scale is a direct functional of the normal-state fit rather than an independent output.

full rationale

The central derivation asserts a universal spectral representation K(ω) = ∫ ρ(γ)/(ω + iγ) dγ for the Cooper kernel directly from microscopic fermionic dynamics, yet supplies no explicit operator or diagrammatic construction isolating ρ(γ) from self-energy or vertices. The superconducting transition scale is then defined as an exponential function of the same infrared TDOS weight that parametrizes normal-state memory kernels, reducing the 'prediction' to a re-expression of the fitted input spectrum.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim rests on a universal spectral representation for the pairing kernel derived from microscopic dynamics, with the TDOS as the characterizing input for relaxation modes; the transition scale is then fixed by the infrared weight of this spectrum.

free parameters (1)
  • infrared TDOS value at zero relaxation rate
    Finite value at vanishing rate is the key input that sets the logarithmic enhancement and exponential transition scale.
axioms (2)
  • standard math Ladder resummation of the pairing vertex together with the Thouless criterion determines the superconducting instability
    Invoked to obtain the transition from the quadratic kernel vanishing.
  • domain assumption Infrared electron dynamics near quantum criticality is generically controlled by the relaxation-rate spectrum
    Assumed to hold for the microscopic fermionic theory without additional mediators.
invented entities (1)
  • Time-scale density of states (TDOS) no independent evidence
    purpose: Spectral representation of collective decay modes that controls both pairing kernel and normal-state response
    Newly introduced as the universal organizing quantity without reference to a specific bosonic mediator.

pith-pipeline@v0.9.0 · 5553 in / 1613 out tokens · 29714 ms · 2026-05-15T19:34:35.390254+00:00 · methodology

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