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arxiv: 2509.04947 · v3 · submitted 2025-09-05 · ❄️ cond-mat.str-el · hep-th· quant-ph

Note on searching for critical lattice models as entropy critical points from strange correlator

Anran Jin , Ling-Yan Hung This is my paper

Pith reviewed 2026-05-18 19:03 UTC · model grok-4.3

classification ❄️ cond-mat.str-el hep-thquant-ph
keywords entropy functioncriticality detectiontopological holographic principletransfer matricesphase diagramscentral chargelattice modelsboundary conditions
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The pith

An entropy function detects criticality in small lattice systems built from topological holography.

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

This note explores using an entropy function from a previous study to find critical points even in small systems. The authors apply this to transfer matrices constructed according to the topological holographic principle. They show that this combination efficiently identifies critical boundary conditions, estimates central charges, and allows mapping out phase diagrams in spaces with multiple parameters. If true, it means researchers can study these models more quickly and with less computational effort than traditional approaches.

Core claim

The authors apply the entropy criticality strategy to lattice transfer matrices from the topological holographic principle and find that the combination provides a cost-effective way to identify critical boundary conditions, estimate central charges, and plot phase diagrams in multi-dimensional phase space.

What carries the argument

entropy function as indicator of criticality applied to transfer matrices constructed via the topological holographic principle

If this is right

  • Critical boundary conditions can be identified efficiently.
  • Central charges can be estimated from the entropy function.
  • Entire phase diagrams can be plotted in multi-dimensional parameter spaces.
  • The method works for small system sizes without large-scale simulations.

Where Pith is reading between the lines

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

  • This approach may generalize to other types of lattice models beyond those from the topological holographic principle.
  • Combining it with other numerical methods could further enhance the search for critical models in condensed matter systems.
  • Validating with finite-size scaling would strengthen confidence in the detected critical points.

Load-bearing premise

The entropy function from the cited work reliably indicates criticality for these topological holographic transfer matrices without extra validation or scaling analysis.

What would settle it

A mismatch between the entropy function's prediction of criticality and results from large-system simulations or exact solutions in the same model would show the method does not work as claimed.

Figures

Figures reproduced from arXiv: 2509.04947 by Anran Jin, Ling-Yan Hung.

Figure 1
Figure 1. Figure 1: FIG. 1: The entropy function Eq. (2) can be defined on (a) an infinite line and (b) a closed circle. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: For each set of {ri}, the value of the entropy function Eq. (2) can be calculated. i.e. The entropy function is a non-linear function of the couplings {ri}. This allows us to search for critical couplings {ri} such that the ground state wavefunction behaves most similarly to a CFT ground state despite the small system size. Moreover, since we consider four equally separated physical sites on a circle, we c… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The entropy function values of the competition between 0 and 0 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The entropy function values of the competition between 0 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: The entropy function values of the competing condensates [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: b plots the entropy function values under the input category Z5 around the theoretical critical point r ∗ = 1/ √ 5 ≈ 0.447. It can be seen that the entropy function still produces a maximum at this first-order critical point, without the ability to distinguish it from second-order critical points. However, it is known that the first order phase transition of the 5-state Potts model is a weak first order tr… view at source ↗
read the original abstract

An entropy function is proposed in [Phys. Rev. Lett. 131, 251602] as a way to detect criticality even when the system size is small. In this note we apply this strategy in the search for criticality of lattice transfer matrices constructed based on the topological holographic principle. We find that the combination of strategy is indeed a cost-effective and efficient way of identifying critical boundary conditions, estimating central charges and moreover, plotting entire phase diagrams in a multi-dimensional phase space.

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 manuscript is a short note applying an entropy function introduced in Phys. Rev. Lett. 131, 251602 to detect criticality in lattice transfer matrices constructed via the topological holographic principle. The authors report that the combination efficiently identifies critical boundary conditions, estimates central charges, and enables plotting of phase diagrams in multi-dimensional parameter spaces.

Significance. If the entropy indicator proves reliable for these holographic transfer matrices, the method could provide a computationally economical route to mapping critical loci and extracting conformal data in lattice models, complementing existing numerical techniques in condensed-matter and holographic contexts. The note highlights a practical synergy between the PRL entropy construction and the authors' prior topological holographic framework.

major comments (2)
  1. Abstract and main text: the claim that the combined strategy is 'cost-effective and efficient' for identifying critical boundary conditions and estimating central charges is asserted without any quantitative benchmarks, error bars, finite-size scaling analysis of the entropy peaks, or direct comparisons to known exactly solvable critical points. This absence leaves open the possibility that observed entropy maxima arise from holographic truncation or boundary artifacts rather than true conformal criticality.
  2. Main text (discussion of the entropy function application): the central empirical observation presupposes that the entropy function from PRL 131, 251602 remains a faithful detector of criticality and central charge when applied to the specific family of transfer matrices generated by the topological holographic principle. No additional validation, such as scaling checks or cross-checks against independent critical-point diagnostics, is supplied to support this transfer of reliability.
minor comments (1)
  1. The manuscript would benefit from a brief explicit statement of the system sizes employed and the precise definition of the entropy function as implemented for the holographic transfer matrices.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and for recognizing the potential utility of combining the entropy indicator with our topological holographic transfer matrices. We address each major comment below and outline revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: Abstract and main text: the claim that the combined strategy is 'cost-effective and efficient' for identifying critical boundary conditions and estimating central charges is asserted without any quantitative benchmarks, error bars, finite-size scaling analysis of the entropy peaks, or direct comparisons to known exactly solvable critical points. This absence leaves open the possibility that observed entropy maxima arise from holographic truncation or boundary artifacts rather than true conformal criticality.

    Authors: We agree that the short note does not include quantitative benchmarks, error bars, or explicit finite-size scaling of the entropy peaks, nor direct numerical comparisons to exactly solvable cases beyond the qualitative identification of known critical boundaries from our prior work. The manuscript is framed as a brief demonstration rather than a comprehensive benchmark study. To address the concern, we will revise the main text to include a representative finite-size scaling analysis for the entropy peaks in one model (e.g., the Ising-like case) and add a direct comparison of the extracted central charge against the known exact value, while discussing possible truncation effects. revision: yes

  2. Referee: Main text (discussion of the entropy function application): the central empirical observation presupposes that the entropy function from PRL 131, 251602 remains a faithful detector of criticality and central charge when applied to the specific family of transfer matrices generated by the topological holographic principle. No additional validation, such as scaling checks or cross-checks against independent critical-point diagnostics, is supplied to support this transfer of reliability.

    Authors: The note applies the PRL entropy function to the new class of holographic transfer matrices without re-deriving its validity from scratch, relying instead on the original validation. We acknowledge that explicit cross-validation in this setting would strengthen the claim. In revision we will add a short paragraph with a scaling check on one known critical point (comparing the entropy-derived central charge to the exact conformal value) and a brief discussion of how boundary artifacts are controlled within the topological holographic construction. revision: yes

Circularity Check

0 steps flagged

No circularity: external entropy function applied to standard holographic transfer matrices

full rationale

The paper imports the entropy function directly from the independent PRL reference [Phys. Rev. Lett. 131, 251602] and applies it to transfer matrices constructed via the topological holographic principle, which is treated as an established construction. No equations or claims reduce by construction to fitted parameters, self-definitions, or load-bearing self-citations whose validity depends on the present work. The central observation—that the combination efficiently identifies critical points and phase diagrams—is presented as an empirical finding rather than a derivation that collapses to its inputs. The paper remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the reliability of the imported entropy function and on the assumption that the topological holographic construction yields transfer matrices whose criticality is correctly captured by that function. No new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption The entropy function defined in Phys. Rev. Lett. 131, 251602 detects criticality for small system sizes in the models considered here.
    Invoked in the first sentence of the abstract as the basis for the search strategy.
  • domain assumption Lattice transfer matrices constructed via the topological holographic principle faithfully represent the boundary physics of interest.
    Stated as the construction method whose criticality is being searched.

pith-pipeline@v0.9.0 · 5603 in / 1431 out tokens · 36694 ms · 2026-05-18T19:03:56.004236+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
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    Relation between the paper passage and the cited Recognition theorem.

    An entropy function is proposed in [Phys. Rev. Lett. 131, 251602] as a way to detect criticality even when the system size is small... we apply this strategy in the search for criticality of lattice transfer matrices constructed based on the topological holographic principle.

What do these tags mean?
matches
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supports
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extends
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uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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