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arxiv: 2605.18391 · v1 · pith:AVPHFFVJnew · submitted 2026-05-18 · 🪐 quant-ph

Reduced-State Stabilizer R\'enyi Entropy as a Probe of Quantum Criticality in the Transverse ANNNI Model and the Quantum Compass Model

Santanu Sarkar , George Biswas , Jun-Yi Wu , Anindya Biswas This is my paper

Pith reviewed 2026-05-20 11:14 UTC · model grok-4.3

classification 🪐 quant-ph
keywords stabilizer Renyi entropyquantum phase transitionstransverse ANNNI modelquantum compass modelreduced density matricesnon-stabilizer resourcesquantum magic
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The pith

The purity-corrected stabilizer Rényi entropy of reduced density matrices detects quantum phase transitions in the transverse ANNNI and quantum compass models.

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

The paper tests whether the stabilizer Rényi entropy, which quantifies non-stabilizer quantum resources, can serve as a detector for quantum phase transitions when computed on reduced portions of the ground state. In the transverse ANNNI model the purity-corrected version locates the antiphase-to-floating transition under high frustration while the uncorrected version better tracks the ferromagnetic-to-paramagnetic boundary under low frustration. In the quantum compass model the corrected entropy produces a distinct feature exactly at the isotropic coupling point that marks a first-order transition. A sympathetic reader would care because the approach ties the distribution of quantum magic inside subsystems to the locations where the entire many-body system changes its phase, supplying an alternative to conventional order parameters or entanglement measures.

Core claim

We investigate the effectiveness of the stabilizer Rényi entropy as an indicator of quantum phase transitions by examining the purity-corrected version applied to reduced density matrices of the ground states. In the transverse axial next-nearest-neighbor Ising model this quantity detects the antiphase-floating transition in the high-frustration regime, while the raw version reproduces the ferromagnetic-paramagnetic boundaries more accurately in the low-frustration regime. In the quantum compass model the purity-corrected entropy exhibits a clear signature near the isotropic point where the system undergoes a first-order transition. These results establish the stabilizer Rényi entropy of the

What carries the argument

the purity-corrected stabilizer Rényi entropy of reduced density matrices, which measures non-stabilizer resources within a subsystem and tracks how that quantity varies with model parameters to locate critical points

If this is right

  • The purity-corrected SRE locates the antiphase-floating transition in the high-frustration regime of the TANNNI model.
  • The raw SRE reproduces the ferromagnetic-paramagnetic phase boundaries in the low-frustration regime of the TANNNI model.
  • The purity-corrected SRE produces a distinct signature at the isotropic point of the quantum compass model.
  • The SRE of reduced states supplies a complementary indicator of quantum criticality and highlights the participation of non-stabilizer resources in many-body phase transitions.

Where Pith is reading between the lines

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

  • The same reduced-state construction could be applied to other frustrated or compass-type Hamiltonians to test whether the detection of transitions remains reliable.
  • If the SRE signature persists under time evolution, it might link non-stabilizer resources to dynamical critical phenomena as well.
  • Direct comparison of the SRE behavior with other quantifiers of magic could clarify whether the reduced-state version captures a unique aspect of the transition.

Load-bearing premise

The assumption that changes in the purity-corrected SRE are caused by the underlying quantum phase transition rather than by finite-size effects or by the specific choice of subsystem size and purity correction procedure.

What would settle it

If the purity-corrected SRE remains smooth and featureless across the known critical values of the coupling parameters when the system size is increased well beyond current exact-diagonalization limits, the claim that it serves as a probe would be falsified.

Figures

Figures reproduced from arXiv: 2605.18391 by Anindya Biswas, George Biswas, Jun-Yi Wu, Santanu Sarkar.

Figure 1
Figure 1. Figure 1: FIG. 1. Phase diagram of the TANNNI model according to [ [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Purity corrected stabilizer R´enyi entropy (in left [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Purity-corrected stabilizer R´enyi entropy of the t [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Purity corrected stabilizer R´enyi entropy (in left [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Phase diagram of the TANNNI model from [ [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Purity corrected stabilizer R´enyi entropy (in left [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Purity corrected stabilizer R´enyi entropy of two qu [PITH_FULL_IMAGE:figures/full_fig_p005_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Purity corrected stabilizer R´enyi entropy (in left [PITH_FULL_IMAGE:figures/full_fig_p006_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Purity uncorrected stabilizer R´enyi entropy (in l [PITH_FULL_IMAGE:figures/full_fig_p007_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Purity corrected stabilizer R´enyi entropy of two q [PITH_FULL_IMAGE:figures/full_fig_p008_14.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Purity uncorrected stabilizer R´enyi entropy (in l [PITH_FULL_IMAGE:figures/full_fig_p008_13.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Purity corrected stabilizer R´enyi entropy of one q [PITH_FULL_IMAGE:figures/full_fig_p009_15.png] view at source ↗
read the original abstract

We investigate the effectiveness of the stabilizer R\'enyi entropy (SRE), a quantifier associated with non-stabilizer resources (quantum magic), as an indicator of quantum phase transitions. Specifically, we analyze the behavior of the purity-corrected SRE of reduced density matrices in the ground states of two one-dimensional spin models: the transverse axial next-nearest-neighbor Ising (TANNNI) model and the quantum compass model (QCM). The ground state of the TANNNI model is obtained using exact diagonalization techniques, while the QCM is analyzed using the Jordan--Wigner (JW) transformation followed by Bogoliubov diagonalization of the resulting quadratic fermionic Hamiltonian. For the TANNNI model, the purity-corrected SRE successfully detects the antiphase--floating phase transition in the high-frustration regime, while in the low-frustration regime the raw (purity-uncorrected) SRE reproduces the known ferromagnetic--paramagnetic phase boundaries more accurately. For the QCM, the purity-corrected SRE exhibits a clear signature near the isotropic point \(J_x/J_z=1\), where the system undergoes a first-order quantum phase transition. Our results establish SRE of reduced states as a complementary probe of quantum criticality and provide further insight into the role of non-stabilizer resources in many-body quantum phase transitions.

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 paper examines the stabilizer Rényi entropy (SRE) of reduced density matrices, with and without purity correction, as a diagnostic for quantum phase transitions in the transverse axial next-nearest-neighbor Ising (TANNNI) model and the quantum compass model (QCM). Ground states of the TANNNI model are obtained via exact diagonalization; the QCM is solved exactly via Jordan-Wigner transformation followed by Bogoliubov diagonalization. The authors report that purity-corrected SRE detects the antiphase-floating transition in the high-frustration regime of TANNNI, while raw SRE better reproduces the ferromagnetic-paramagnetic boundary at low frustration; in the QCM a clear signature appears at the isotropic point Jx/Jz = 1 marking the first-order transition.

Significance. If the reported SRE signatures prove robust under finite-size scaling and independent of subsystem partition, the work would supply a concrete numerical example linking non-stabilizer resources to quantum criticality and could motivate further analytic or tensor-network studies of magic as an order parameter. The exact solvability of the QCM provides a useful benchmark, while the TANNNI results illustrate regime-dependent utility of the purity correction.

major comments (2)
  1. [TANNNI results] TANNNI results (exact-diagonalization section): the manuscript presents SRE data only for small finite L without any finite-size scaling, data collapse, or extrapolation to the thermodynamic limit. Because the claimed detection of the antiphase-floating transition rests on these finite-L signatures, the absence of scaling analysis leaves open the possibility that the observed features are finite-size artifacts rather than universal indicators of the transition.
  2. [QCM results] QCM results (exact-solution section): the reduced-state SRE is computed for a specific subsystem partition whose size and location are not varied. No demonstration is given that the signature at Jx/Jz = 1 survives changes in subsystem size or is independent of the chosen cut, which is required to establish that the feature is a property of the phase transition rather than of the particular reduced-state choice.
minor comments (2)
  1. [Notation] Notation for the purity-corrected SRE should be defined once in the methods section and used consistently; the abstract and main text occasionally switch between “purity-corrected SRE” and “corrected SRE” without cross-reference.
  2. [Figures] Figure captions for the TANNNI SRE plots should explicitly state the system sizes L employed and whether open or periodic boundaries were used.

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, indicating where revisions will be made to improve the presentation and robustness of our results.

read point-by-point responses

  1. Referee: [TANNNI results] TANNNI results (exact-diagonalization section): the manuscript presents SRE data only for small finite L without any finite-size scaling, data collapse, or extrapolation to the thermodynamic limit. Because the claimed detection of the antiphase-floating transition rests on these finite-L signatures, the absence of scaling analysis leaves open the possibility that the observed features are finite-size artifacts rather than universal indicators of the transition.

    Authors: We agree that finite-size scaling analysis would strengthen the claim that the SRE signatures reflect the antiphase-floating transition rather than finite-size effects. Our TANNNI results rely on exact diagonalization, which limits us to modest system sizes (L up to 12–16). In the revised manuscript we will add data for several values of L, track the location and height of the SRE features as functions of L, and include a brief extrapolation or convergence discussion toward the thermodynamic limit. Full data collapse may remain limited by the accessible sizes, but the added analysis will clarify the robustness of the reported detection. revision: yes

  2. Referee: [QCM results] QCM results (exact-solution section): the reduced-state SRE is computed for a specific subsystem partition whose size and location are not varied. No demonstration is given that the signature at Jx/Jz = 1 survives changes in subsystem size or is independent of the chosen cut, which is required to establish that the feature is a property of the phase transition rather than of the particular reduced-state choice.

    Authors: We thank the referee for highlighting this point. Because the QCM is solved exactly via the Jordan–Wigner transformation, the reduced SRE can be recomputed for arbitrary subsystem sizes and locations without additional numerical cost. In the revised manuscript we will present results for several contiguous and non-contiguous partitions (varying both the number of sites and their position along the chain) and show that the discontinuity or peak at Jx/Jz = 1 remains stable, thereby confirming that the signature is tied to the first-order transition rather than to the specific cut chosen. revision: yes

Circularity Check

0 steps flagged

No significant circularity; numerical probe compares SRE to external phase boundaries

full rationale

The paper computes the purity-corrected stabilizer Rényi entropy of reduced density matrices for ground states obtained via exact diagonalization (TANNNI) and Jordan-Wigner plus Bogoliubov diagonalization (QCM). These are direct numerical evaluations of a defined quantity on model Hamiltonians whose phase boundaries are taken from prior independent literature. No equation reduces a claimed prediction to a fitted parameter inside the paper, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz is smuggled via prior work by the same authors. The study is therefore self-contained against external benchmarks and receives the default low-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The abstract supplies no explicit free parameters, axioms, or invented entities. The work rests on standard quantum mechanics, the definition of stabilizer Rényi entropy from prior literature, and the accuracy of exact diagonalization and Jordan-Wigner methods for the chosen system sizes.

axioms (1)
  • domain assumption Ground states of the TANNNI and QCM Hamiltonians are accurately obtained by exact diagonalization and Jordan-Wigner plus Bogoliubov diagonalization respectively.
    Stated in the abstract as the computational route used to access the ground states.

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