arxiv: 2605.00091 · v1 · submitted 2026-04-30 · ❄️ cond-mat.dis-nn · cond-mat.stat-mech

Recognition: unknown

Locality versus Fock-space structure in East-type models

Achilleas Lazarides

Pith reviewed 2026-05-09 20:21 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn cond-mat.stat-mech

keywords East modelFock spacemany-body localizationkinetic constraintslocalization transitionquantum many-body systemsconstrained dynamicsHilbert space graph

0 comments

The pith

Randomizing Fock-space connections in the quantum East model while preserving magnetization sectors still yields a delocalized-to-localized transition.

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

The paper modifies the quantum East model by randomizing how states connect in Fock space, breaking geometric locality of spin flips in real space. It keeps the organization into neighboring magnetization sectors intact. This randomized version still shows a clear phase transition between a delocalized phase and a localized phase. A sympathetic reader would care because the result isolates the Fock-space graph structure as the driver of the transition, rather than the original spatial constraints. This reframes what causes slow dynamics or many-body localization in kinetically constrained systems.

Core claim

By randomizing the connectivity in Fock space while preserving its organisation into neighbouring magnetisation sectors, the modified East model still exhibits a transition between two distinct phases, one delocalised and the other localised. The authors conclude that, for East-type constrained models, the essential ingredient is the structure of the graph in Fock space rather than geometric locality of spin flips.

What carries the argument

The randomized Fock-space connectivity graph that preserves neighboring magnetization sectors, which carries the argument by decoupling real-space locality from the constraint-induced phase transition.

If this is right

Localization transitions in other East-type models arise primarily from the global Fock-space graph rather than local flip rules.
Slow relaxation in constrained quantum systems can be analyzed through random-matrix properties of the effective Hilbert-space graph.
Models without geometric locality can still host many-body localization if their Fock-space connectivity matches the sector-organized pattern.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This approach could extend to other kinetically constrained models to test whether Fock-space structure universally overrides spatial details.
Analytic random-matrix predictions might now be applied directly to the randomized version to locate the transition point without spatial geometry.

Load-bearing premise

The randomization of connections preserves a meaningful comparison to the original East model without introducing artifacts that create the observed transition.

What would settle it

Numerical evidence that the delocalized-localized transition disappears when the randomization is altered to break the neighboring magnetization sector structure while keeping the same overall connectivity density.

Figures

Figures reproduced from arXiv: 2605.00091 by Achilleas Lazarides.

**Figure 2.** Figure 2: Panels (a-c) show the locations of the nonzero matrix elements in the Hamiltonians of the standard Ising, quantum [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: Infinite-time average of the dynamical participation ratio [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: Representative examples of the Shannon entropy [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: Mean scaled Shannon entropy µS/ ln D for the East (panel (a)) and permuted East (b) models, averaged over all eigenstates and disorder realisations (number of realisations indicated in the legend) for each size L. Here w = 1. As s increases the mean decreases, consistent with increasing localisation. For a quantitative determination of the transition point see [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 6.** Figure 6: Local spectral variance σ 2 S (Eq. 8), averaged over all eigenstates and disorder realisations (number of realisations indicated in the legend), for a number of system sizes L. Here w = 1. Panels (a) and (b) show σ 2 S for the East and permuted East models. Both display a reversal of the trend with system size at some s, indicating a transition from an delocalised to a localised phase, and a broad maximum … view at source ↗

read the original abstract

Local kinetic constraints in quantum many-body systems can generate slow dynamics or complete many-body localisation. Here we focus on a modification of the quantum East model: Inspired by random matrix theory, we randomise the connectivity in Fock space (rendering it nonlocal in real space) while preserving its organisation into neighbouring magnetisation sectors. We find that there is still a transition between two distinct phases, one delocalised and the other localised. We conclude that, for East-type constrained models, the essential ingredient is the structure of the graph in Fock space rather than geometric locality of spin flips.

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 / 1 minor

Summary. The paper modifies the quantum East model by randomizing Fock-space connectivity (inspired by random matrix theory) while preserving organization into neighboring magnetization sectors. Numerical observations indicate that a delocalized-to-localized transition persists in this nonlocal version, leading to the conclusion that the essential ingredient for East-type dynamics is the structure of the graph in Fock space rather than geometric locality of the spin flips.

Significance. If the result holds, the work offers a valuable test of whether real-space locality or abstract Fock-space organization drives the slow dynamics and localization in kinetically constrained models. The randomization approach provides a concrete way to isolate these factors, with potential implications for many-body localization theory and the design of constrained quantum systems. The idea is conceptually clean and could stimulate further graph-theoretic analyses of Hilbert-space dynamics.

major comments (2)

[Model definition and randomization procedure] The randomization procedure (model section) reassigns allowed flips between neighboring magnetization sectors but does not report controls ensuring preservation of the original degree distribution, one-way facilitation bias, or hierarchical constraint structure of the East model. Without these invariants, changes in average connectivity or directionality could produce a delocalized phase for reasons unrelated to Fock-space organization, weakening the claim that locality is inessential.
[Numerical results] The results section reports that a transition is still observed but supplies no details on system sizes, numerical methods (e.g., exact diagonalization or time evolution), localization diagnostics (participation ratio, level statistics, or entanglement), or error analysis. This absence prevents assessment of whether the phases are robustly identified and directly comparable to the original East model.

minor comments (1)

[Abstract] The abstract would benefit from a brief mention of the specific observable or diagnostic used to detect the transition.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive evaluation of the significance of our work and for the constructive comments. We address each major point below and have revised the manuscript to provide the requested clarifications and details.

read point-by-point responses

Referee: [Model definition and randomization procedure] The randomization procedure (model section) reassigns allowed flips between neighboring magnetization sectors but does not report controls ensuring preservation of the original degree distribution, one-way facilitation bias, or hierarchical constraint structure of the East model. Without these invariants, changes in average connectivity or directionality could produce a delocalized phase for reasons unrelated to Fock-space organization, weakening the claim that locality is inessential.

Authors: We appreciate the referee drawing attention to this aspect of the procedure. The randomization reassigns connections exclusively within the same pairs of neighboring magnetization sectors while exactly preserving the number of allowed flips outgoing from each Fock-space state; this construction maintains the original degree distribution, the unidirectional facilitation bias (flips remain possible only in the direction permitted by the East constraint), and the overall hierarchical sector organization. These invariants were verified during model construction but were not explicitly documented. In the revised manuscript we have added a dedicated paragraph in the model section describing the randomization algorithm step by step together with supplementary verification plots confirming that the degree distribution and bias are identical to those of the original quantum East model. We believe these additions remove any ambiguity and reinforce that the persistence of the transition arises from the retained Fock-space graph structure. revision: yes
Referee: [Numerical results] The results section reports that a transition is still observed but supplies no details on system sizes, numerical methods (e.g., exact diagonalization or time evolution), localization diagnostics (participation ratio, level statistics, or entanglement), or error analysis. This absence prevents assessment of whether the phases are robustly identified and directly comparable to the original East model.

Authors: We agree that the numerical implementation was described too briefly. The revised manuscript now contains an expanded 'Numerical Methods' subsection that specifies the system sizes employed, the use of exact diagonalization to obtain eigenstates, the localization diagnostics (inverse participation ratio and adjacent-gap ratio for level statistics), and the error analysis obtained by averaging over multiple independent realizations of the randomized connectivity. A direct side-by-side comparison of the critical point and diagnostic values with the standard quantum East model has also been included. These additions enable a clear assessment of robustness and comparability. revision: yes

Circularity Check

0 steps flagged

No circularity: conclusion follows from explicit model randomization and observed transition

full rationale

The paper constructs a randomized Fock-space graph that preserves only magnetization-sector adjacency, simulates the dynamics, and reports a delocalized-to-localized transition. The claim that Fock-space structure (rather than real-space locality) is essential is a direct inference from this controlled modification and its phenomenology. No equation reduces to a fitted parameter defined from the target result, no self-citation supplies a uniqueness theorem, and no ansatz is smuggled in. The derivation chain is self-contained and externally falsifiable via the randomization procedure itself.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; no explicit free parameters, axioms, or invented entities are stated. The model modification itself implicitly assumes that preserving magnetization sectors is sufficient to retain East-type physics.

pith-pipeline@v0.9.0 · 5386 in / 1030 out tokens · 22430 ms · 2026-05-09T20:21:29.747736+00:00 · methodology

discussion (0)

Reference graph

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