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arxiv: 2605.20656 · v1 · pith:5DD3X4VOnew · submitted 2026-05-20 · 🪐 quant-ph · cond-mat.dis-nn

Entanglement Growth from Structured Initial States in Many-Body Localized Systems

Chen Xu , Pengfei Zhang This is my paper

Pith reviewed 2026-05-21 05:31 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.dis-nn
keywords many-body localizationentanglement growthWehrl-Rényi entropystructured initial statesrandom-field XXZ modellocal integrals of motionmultipartite entanglement
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The pith

Structured initial states produce non-monotonic entanglement growth in many-body localized systems when product states are polarized along z.

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

The paper examines how varying the initial entanglement in structured states affects subsequent entanglement growth in many-body localized systems. Using the random-field XXZ model, it demonstrates that the net growth of Wehrl-Rényi entropy for z-polarized product states increases then decreases with rising initial entanglement. The first regime is driven by finite magnetization tied to local integrals of motion, while the second arises from inter-site correlations. For x- or y-polarized product states the growth instead falls monotonically. This distinction clarifies how different initial-state features control the buildup of multipartite entanglement in localized phases.

Core claim

The non-monotonic dependence of total entanglement entropy growth on initial entanglement, previously noted for chaotic-to-MBL quenches, also occurs in the Wehrl-Rényi entropy for z-directed product states. The first regime is governed by a finite magnetization associated with local integrals of motion, while the second reflects inter-site correlations. In contrast, product states polarized along x or y show only monotonic decay of entanglement growth.

What carries the argument

Dynamics of the Wehrl-Rényi entropy as a multipartite-entanglement proxy, tracked under quench from structured initial states in the random-field XXZ model.

Load-bearing premise

The random-field XXZ model at the chosen disorder strength and finite system size captures generic many-body localized behavior, and the Wehrl-Rényi entropy is an appropriate proxy for multipartite entanglement growth.

What would settle it

Numerical or experimental data showing strictly monotonic Wehrl-Rényi entropy growth versus initial entanglement for z-polarized states, without the reported up-then-down behavior across a range of preparation times, would falsify the claimed two-regime structure.

Figures

Figures reproduced from arXiv: 2605.20656 by Chen Xu, Pengfei Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of our setup. We consider the [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The evolution of the HCEE, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) The averaged local magnetization [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The total entanglement growth of both the HCEE [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The total entanglement growth of both the HCEE [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

Understanding how complex entanglement structures emerge is a central problem in quantum many-body physics. Recent work by Zhang et al. has considered structured initial states prepared by evolving a product state under a chaotic Hamiltonian for a finite time before quenching to the target Hamiltonian. In this setup, total entanglement entropy growth in many-body localized systems exhibits two distinct regimes, first increasing and then decreasing as the initial entanglement is tuned. In this work, we identify the physical origin of this behavior by analyzing the dynamics of both the R\'enyi entanglement entropy and the Wehrl-R\'enyi entropy in the random-field XXZ model, the latter of which characterizes multipartite entanglement. We show that a similar non-monotonic dependence on the initial entanglement also appears in the net growth of the Wehrl-R\'enyi entropy for product states polarized along the $z$-direction. The first regime is governed by a finite magnetization associated with local integrals of motion, while the second reflects inter-site correlations. In contrast, for product states in the $x/y$-direction, the entanglement growth exhibits a monotonic decay. Our results provide a more fine-grained picture of how distinct initial-state properties shape entanglement dynamics in many-body localized systems.

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 studies entanglement dynamics in many-body localized (MBL) systems prepared from structured initial states, obtained by evolving product states under a chaotic Hamiltonian before quenching to the random-field XXZ model. It reports that the Wehrl-Rényi entropy (used as a proxy for multipartite entanglement) exhibits non-monotonic growth with increasing initial entanglement for z-polarized states, with the first regime attributed to finite magnetization from local integrals of motion (LIOMs) and the second to inter-site correlations; x/y-polarized states instead show monotonic decay. This refines earlier observations on total Rényi entanglement entropy.

Significance. If the central attribution holds, the work supplies a useful separation of magnetization versus correlation contributions to entanglement growth in MBL systems and demonstrates the utility of the Wehrl-Rényi entropy for tracking multipartite structure. Such distinctions could help characterize the role of LIOMs in realistic finite-size numerics.

major comments (2)
  1. [§3] §3 (Numerical setup): The chosen disorder strength and system sizes for the random-field XXZ chain are not accompanied by standard MBL diagnostics (Poisson level statistics, eigenstate entanglement scaling, or localization length ≪ L). Because the first regime is explicitly attributed to conserved magnetization from LIOMs, the absence of these checks leaves open the possibility that the observed non-monotonicity arises from slow thermalization or prethermal effects instead.
  2. [Results on Wehrl-Rényi entropy] Results on Wehrl-Rényi entropy (around the discussion of net growth for z-polarized states): The mapping from the second regime to inter-site correlations is stated but not supported by an explicit decomposition or comparison against a magnetization-subtracted observable; without this, the separation between the two regimes remains interpretive rather than quantitative.
minor comments (2)
  1. [Figures] Figure captions and methods: Add the number of disorder realizations and any error-bar information; the current presentation leaves the statistical robustness of the non-monotonic curves unclear.
  2. [Main text] Notation: Define the precise normalization or subtraction used for “net growth” of the Wehrl-Rényi entropy when it is first introduced in the main text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments. We address each major point below and describe the revisions we will make to the manuscript.

read point-by-point responses

  1. Referee: [§3] §3 (Numerical setup): The chosen disorder strength and system sizes for the random-field XXZ chain are not accompanied by standard MBL diagnostics (Poisson level statistics, eigenstate entanglement scaling, or localization length ≪ L). Because the first regime is explicitly attributed to conserved magnetization from LIOMs, the absence of these checks leaves open the possibility that the observed non-monotonicity arises from slow thermalization or prethermal effects instead.

    Authors: We agree that explicit MBL diagnostics would strengthen the attribution to local integrals of motion and help rule out alternative explanations. In the revised manuscript we will add the average level-spacing ratio (confirming Poisson statistics), the scaling of eigenstate entanglement entropy with system size, and an estimate of the localization length for the disorder strengths and system sizes used in the numerics. revision: yes

  2. Referee: [Results on Wehrl-Rényi entropy] Results on Wehrl-Rényi entropy (around the discussion of net growth for z-polarized states): The mapping from the second regime to inter-site correlations is stated but not supported by an explicit decomposition or comparison against a magnetization-subtracted observable; without this, the separation between the two regimes remains interpretive rather than quantitative.

    Authors: The separation is currently supported by the contrasting dynamics: non-monotonic net growth appears only for z-polarized states (which carry finite magnetization tied to LIOMs) while x/y-polarized states exhibit monotonic decay. We nevertheless acknowledge that an explicit quantitative decomposition would make the claim more rigorous. In the revision we will include a direct comparison against a magnetization-subtracted observable to quantify the inter-site correlation contribution in the second regime. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on direct numerical observables

full rationale

The paper analyzes Rényi and Wehrl-Rényi entropy dynamics via numerical simulation of the random-field XXZ model. The non-monotonic regimes for z-polarized states are attributed to observed finite magnetization (linked to LIOMs) versus inter-site correlations, while x/y states show monotonic decay. These distinctions derive from explicit dynamical quantities and state polarizations rather than any redefinition of fitted initial entanglement or self-referential inputs. The reference to 'Zhang et al.' supplies setup context for structured states but is not load-bearing for the new origin claims. No self-definitional loops, fitted predictions, or ansatz smuggling appear in the provided text or abstract.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The analysis rests on standard many-body localization assumptions (existence of local integrals of motion, slow entanglement growth) and on the interpretation of Wehrl-Rényi entropy as a multipartite measure; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Local integrals of motion exist and produce a finite magnetization that survives in the MBL phase.
    Invoked to explain the first regime of non-monotonic growth.
  • domain assumption The random-field XXZ Hamiltonian realizes generic many-body localization.
    Used as the concrete model for all reported dynamics.

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discussion (0)

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