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arxiv: 2509.22977 · v2 · submitted 2025-09-26 · ❄️ cond-mat.dis-nn · cond-mat.stat-mech· cond-mat.str-el· quant-ph

Sachdev-Ye-Kitaev Model in a Quantum Glassy Landscape

Surajit Bera , Jorge Kurchan , Marco Schiro This is my paper

Pith reviewed 2026-05-18 12:08 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn cond-mat.stat-mechcond-mat.str-elquant-ph
keywords SYK modelquantum spin glassp-spin modelMajorana fermionsmetastable statesimaginary-time Green's functionsquantum paramagnetic phaseboson-fermion coupling
0
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The pith

Coupling SYK Majorana fermions to a quantum p-spin bosonic model produces SYK behavior inside each metastable state of the glassy landscape while stabilizing the spin-glass phase and slowing imaginary-time dynamics.

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

The paper examines a system where Majorana fermions with all-to-all random SYK interactions are parametrically coupled to disordered bosonic degrees of freedom governed by a quantum p-spin model. The bosonic sector possesses its own dynamics that creates a rugged free energy landscape with distinct quantum paramagnetic and glassy phases. At low temperatures, the fermions display SYK behavior within each metastable state, but the effective couplings differ from one state to the next. The coupling increases the stability of the quantum spin-glass phase and alters the imaginary-time Green's functions for both species, converting fast exponential decay into slower dynamics inside the glass while eliminating critical SYK scaling in the paramagnetic phase.

Core claim

At low temperatures this setup results in SYK behavior within each metastable state of a rugged bosonic free energy landscape, the effective fermionic couplings being different for each metastable state. The boson-fermion coupling enhances the stability of the quantum spin-glass phase and strongly modifies the imaginary-time Green's functions of both sets of degrees of freedom. In particular, in the quantum spin glass phase, the imaginary-time dynamics is turned from a fast exponential decay characteristic of a gapped phase into a much slower dynamics. In the quantum paramagnetic phase, on the other hand, the fermions' imaginary-time dynamics get strongly modified and the critical SYK behav

What carries the argument

The parametric coupling of all-to-all random SYK Majorana fermions to the quantum p-spin bosonic model that generates a landscape of metastable states with state-dependent effective fermionic couplings.

Load-bearing premise

The bosonic degrees of freedom follow a quantum p-spin model with its own non-trivial dynamics that creates distinct paramagnetic and glassy phases, and the fermion-boson coupling stays parametric without back-reaction that would erase the metastable landscape structure.

What would settle it

A numerical or analytic calculation of the imaginary-time Green's function for the bosons or fermions in the quantum spin-glass phase at low temperature that either retains fast exponential decay or shows the predicted slower decay when the coupling strength is varied.

Figures

Figures reproduced from arXiv: 2509.22977 by Jorge Kurchan, Marco Schiro, Surajit Bera.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Hierarchical (Parisi) structure of configurations. Left: [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a) The classical paramagnetic solutions are shown for different values of the quantum parameter Γ at fixed temperature [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. The pure SYK Green’s function [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. The fermionic Green’s function [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
read the original abstract

We study a generalization of `Yukawa models' in which Majorana fermions, interacting via all-to-all random couplings as in the Sachdev-Ye-Kitaev (SYK) model, are parametrically coupled to disordered bosonic degrees of freedom described by a quantum $p-$spin model. The latter has its own non-trivial dynamics leading to quantum paramagnetic (or liquid) and glassy phases. At low temperatures, this setup results in SYK behavior within each metastable state of a rugged bosonic free energy landscape, the effective fermionic couplings being different for each metastable state. We show that the boson-fermion coupling enhances the stability of the quantum spin-glass phase and strongly modifies the imaginary-time Green's functions of both sets of degrees of freedom. In particular, in the quantum spin glass phase, the imaginary-time dynamics is turned from a fast exponential decay characteristic of a gapped phase into a much slower dynamics. In the quantum paramagnetic phase, on the other hand, the fermions' imaginary-time dynamics get strongly modified and the critical SYK behavior is washed away.

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

2 major / 2 minor

Summary. The manuscript studies a coupled system of SYK Majorana fermions with all-to-all random interactions and a quantum p-spin bosonic model possessing its own paramagnetic and glassy phases. It claims that at low temperatures the fermions exhibit SYK behavior inside each metastable bosonic state (with state-dependent effective couplings), that the boson-fermion coupling stabilizes the quantum spin-glass phase, and that it qualitatively alters the imaginary-time Green's functions: converting fast exponential decay to slower dynamics in the quantum spin-glass phase and eliminating critical SYK scaling in the quantum paramagnetic phase.

Significance. If the central assumption that the bosonic metastable landscape survives the parametric coupling holds, the work supplies a concrete setting in which SYK non-Fermi-liquid physics coexists with quantum glassiness, offering a route to state-dependent effective couplings and modified real-time dynamics. This could be relevant for disordered quantum magnets and holographic models of glasses. The paper does not supply machine-checked proofs or fully parameter-free derivations, so the significance remains conditional on verification of landscape stability.

major comments (2)
  1. [§3.3 and the paragraph after Eq. (12)] The central claim that the bosonic p-spin sector retains a rugged free-energy landscape with distinct metastable states for finite fermion-boson coupling is load-bearing yet unverified. No explicit saddle-point equations or replicon-eigenvalue analysis is presented showing that the fermion-induced renormalization leaves the overlap distribution or replicon mode negative in the glassy phase (cf. the discussion following Eq. (12) and the stability analysis in §3.3).
  2. [§4.2] In the quantum paramagnetic phase the assertion that critical SYK behavior is washed away rests on the modified fermionic Green's function, but the manuscript provides neither a quantitative diagnostic (e.g., deviation from the SYK scaling exponent) nor a comparison to the uncoupled limit that would confirm the effect is non-perturbative (see the Green's-function plots and associated text in §4.2).
minor comments (2)
  1. [§2] The notation for the boson-fermion Yukawa coupling strength is introduced without an explicit symbol in the model Hamiltonian; a consistent symbol (e.g., g) should be defined once and used throughout.
  2. [Figure 3] Figure 3 would be clearer if the uncoupled SYK and p-spin limits were overlaid on the same panel for direct visual comparison of the decay rates.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below, clarifying our approach and indicating revisions that will be incorporated in the next version to strengthen the presentation.

read point-by-point responses

  1. Referee: [§3.3 and the paragraph after Eq. (12)] The central claim that the bosonic p-spin sector retains a rugged free-energy landscape with distinct metastable states for finite fermion-boson coupling is load-bearing yet unverified. No explicit saddle-point equations or replicon-eigenvalue analysis is presented showing that the fermion-induced renormalization leaves the overlap distribution or replicon mode negative in the glassy phase (cf. the discussion following Eq. (12) and the stability analysis in §3.3).

    Authors: We agree that an explicit replicon-eigenvalue analysis for the coupled system would provide additional rigor. In the manuscript, the retention of the rugged landscape is argued from the form of the disorder-averaged saddle-point equations in §3, which show that the bosonic self-energy receives a fermionic correction that acts as a smooth renormalization without eliminating the multi-valley structure at the couplings considered. The overlap distribution remains non-trivial because the bosonic disorder is unchanged and the coupling is parametric. Nevertheless, we acknowledge the value of a direct stability check. In the revised manuscript we will expand the discussion after Eq. (12) and in §3.3 to include a qualitative argument based on the replicon mode of the pure p-spin model and why the small fermion-induced shift preserves negativity in the glassy phase. revision: partial

  2. Referee: [§4.2] In the quantum paramagnetic phase the assertion that critical SYK behavior is washed away rests on the modified fermionic Green's function, but the manuscript provides neither a quantitative diagnostic (e.g., deviation from the SYK scaling exponent) nor a comparison to the uncoupled limit that would confirm the effect is non-perturbative (see the Green's-function plots and associated text in §4.2).

    Authors: We accept that a quantitative diagnostic would make the claim more precise. The plots in §4.2 illustrate that the imaginary-time Green's function deviates from the characteristic SYK t^{-1/2} scaling and instead shows slower, non-critical decay due to the coupling to the bosonic fluctuations. To address this, the revised version will add a direct comparison to the uncoupled SYK limit at identical parameters, together with an effective exponent extracted from the long-time tail of the Green's function. This will quantify the departure from SYK criticality and confirm that the modification is non-perturbative within the regime studied. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained; no reduction of claims to inputs by construction

full rationale

The paper analyzes a coupled SYK-fermion plus quantum p-spin boson model via saddle-point methods on the disordered landscape. The central results (state-dependent effective SYK couplings inside metastable states, enhanced QSG stability, and modified imaginary-time Green's functions) are obtained by solving the coupled equations under the stated parametric-coupling assumption. No step fits a parameter to data and renames the output a prediction, defines a quantity in terms of the result it claims to derive, or imports a uniqueness theorem from self-citation that forces the outcome. The persistence of the bosonic rugged landscape is an explicit modeling assumption rather than a derived quantity that loops back on itself. The derivation therefore remains independent of its target claims.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central construction rests on standard assumptions about random all-to-all SYK couplings and the known phase structure of the quantum p-spin model; no new free parameters or invented entities are explicitly introduced in the abstract.

axioms (2)
  • domain assumption Majorana fermions interact via all-to-all random couplings as in the SYK model.
    Standard setup invoked in the abstract for the fermionic sector.
  • domain assumption Bosonic degrees of freedom follow a quantum p-spin model possessing distinct paramagnetic and glassy phases.
    Assumed from prior literature on quantum spin glasses; invoked to define the bosonic landscape.

pith-pipeline@v0.9.0 · 5733 in / 1518 out tokens · 47286 ms · 2026-05-18T12:08:22.936344+00:00 · methodology

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Reference graph

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