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arxiv: 2605.27350 · v1 · pith:754WBLNI · submitted 2026-05-26 · quant-ph · cond-mat.mes-hall· cond-mat.stat-mech· cond-mat.str-el

Postselection-free ballistic-diffusive transition in monitored spin chains

K. G. S. H. Gunawardana , Ali G. Moghaddam , Teemu Ojanen This is my paper

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classification quant-ph cond-mat.mes-hallcond-mat.stat-mechcond-mat.str-el
keywords monitored quantum systemsmeasurement-induced phase transitionsballistic-diffusive transitiondomain wall dynamicsentanglement transitionXXZ spin chainmany-body Zeno effect
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The pith

In monitored XXZ spin chains a ballistic-to-diffusive transition in domain-wall spreading coincides with the entanglement phase transition and appears without postselection.

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

The paper studies spin and entanglement dynamics in spin-1/2 XXZ chains under periodic monitoring. It finds that an initial domain wall spreads ballistically at low monitoring rates and diffusively at high rates. This change in transport coincides with the steady-state entanglement phase transition. Because the domain-wall dynamics can be measured in the unconditioned evolution, the transition provides an experimentally accessible signature of the many-body Zeno effect that does not require postselection on measurement outcomes.

Core claim

The authors show that periodically monitored XXZ chains exhibit a measurement-induced entanglement phase transition together with a ballistic-to-diffusive transition in the transient spreading of a domain wall. Extensive numerics and theoretical arguments indicate that the two transitions are intimately interlinked, so that the postselection-free domain-wall dynamics serve as a direct probe of the entanglement criticality.

What carries the argument

The initial domain-wall state |↑↑↑…↓↓↓…⟩ whose spreading velocity changes from ballistic to diffusive at the critical monitoring rate that also marks the entanglement transition.

If this is right

  • The entanglement transition can be detected through spin-density or magnetization profiles without postselection.
  • Periodic monitoring provides a tunable knob between ballistic and diffusive transport in monitored spin chains.
  • The many-body Zeno effect appears directly in the slowing of domain melting as monitoring increases.
  • Similar postselection-free signatures may exist in other monitored many-body systems.

Where Pith is reading between the lines

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

  • Monitoring strength could be used to control the speed of information or excitation propagation in quantum simulators.
  • Classical-like transport measurements might serve as a proxy for entanglement criticality in larger systems.
  • The coincidence of the two transitions could be tested by varying the monitoring protocol or initial-state preparation.

Load-bearing premise

The transient domain-wall dynamics in the unconditioned evolution reflect the same critical monitoring rate as the postselected steady-state entanglement transition.

What would settle it

A numerical or experimental measurement showing that the monitoring rate at which domain-wall spreading becomes diffusive differs from the rate at which the steady-state entanglement entropy changes its scaling.

Figures

Figures reproduced from arXiv: 2605.27350 by Ali G. Moghaddam, K. G. S. H. Gunawardana, Teemu Ojanen.

Figure 1
Figure 1. Figure 1: FIG. 1. Ballistic to diffusive transition in periodically mon [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Dynamics of spin chains in the high-frequency moni [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Entanglement dynamics and entanglement phase transitions. (a)-(d): Entanglement entropy as a function of time [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Temporal spreading of the spin up domain for different monitoring strengths. (a): Dots correspond to the actual data [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Scaling analysis of the magnetization dynamics. (a): [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

We study spin and entanglement dynamics in spin-1/2 XXZ chains under periodic monitoring and show that this system exhibits two measurement-induced phase transitions: a steady-state entanglement phase transition similar to those in monitored quantum circuits and a ballistic-to-diffusive transition in transient dynamics. Specifically, we discover that at low monitoring rate, an initial configuration containing a domain wall $|\uparrow\uparrow\uparrow\ldots \downarrow\downarrow\downarrow\ldots\rangle$ spreads ballistically while, at large monitoring rates, the domain melting is diffusive. Extensive numerical simulations, supported by theoretical arguments, indicate that the ballistic-diffusive transition is intimately interlinked with the entanglement phase transition. In contrast to the entanglement phase transitions, which require exponentially complex postselection, the ballistic-diffusive transition can be observed without postselection and constitutes an experimentally accessible manifestation of the many-body Zeno effect.

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

1 major / 2 minor

Summary. The manuscript examines periodically monitored spin-1/2 XXZ chains and reports two measurement-induced transitions: a steady-state entanglement phase transition (requiring postselection) and a ballistic-to-diffusive transition in the transient spreading of a domain-wall initial state. Extensive numerics and theoretical arguments are presented to show that the ballistic-diffusive transition occurs at the same critical monitoring rate as the entanglement transition and can be observed in the unconditioned Lindblad evolution without postselection, serving as an experimentally accessible manifestation of the many-body Zeno effect.

Significance. If the reported coincidence of critical monitoring rates is confirmed, the result provides a postselection-free dynamical probe of measurement-induced criticality. This is significant because postselection on rare trajectories is experimentally prohibitive, while domain-wall spreading in the average dynamics is directly measurable in quantum simulators. The approach links transient transport to steady-state entanglement scaling in a concrete spin-chain model.

major comments (1)
  1. [Numerical results and discussion of critical rates] The central claim of an 'intimate interlink' between the ballistic-diffusive and entanglement transitions requires explicit demonstration that the critical monitoring rate extracted from domain-wall spreading in the unconditioned (Lindblad) dynamics coincides with the critical rate from postselected entanglement entropy. The manuscript should report the two critical values (with uncertainty estimates from finite-size scaling or fitting) side-by-side, e.g., in a dedicated table or figure panel, because the Lindblad master equation for the averaged state differs from the conditioned trajectory ensemble and nothing a priori guarantees exact equality.
minor comments (2)
  1. [Model definition] Clarify the precise form of the periodic monitoring operators and the XXZ anisotropy parameter used in the simulations.
  2. [Figures] Ensure that all plots of domain-wall width or velocity versus monitoring rate include the extracted critical point with error bars for direct visual comparison with the entanglement data.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive assessment of our work and for the constructive suggestion to strengthen the presentation of our central claim. We address the major comment below.

read point-by-point responses

  1. Referee: [Numerical results and discussion of critical rates] The central claim of an 'intimate interlink' between the ballistic-diffusive and entanglement transitions requires explicit demonstration that the critical monitoring rate extracted from domain-wall spreading in the unconditioned (Lindblad) dynamics coincides with the critical rate from postselected entanglement entropy. The manuscript should report the two critical values (with uncertainty estimates from finite-size scaling or fitting) side-by-side, e.g., in a dedicated table or figure panel, because the Lindblad master equation for the averaged state differs from the conditioned trajectory ensemble and nothing a priori guarantees exact equality.

    Authors: We agree that an explicit side-by-side comparison of the two critical monitoring rates, including uncertainty estimates, would make the claimed interlink more transparent. Although our extensive numerics and theoretical arguments already indicate coincidence of the transitions, we will revise the manuscript to include a dedicated table or figure panel reporting the critical value from domain-wall spreading in the Lindblad dynamics next to the value from postselected entanglement entropy, each with uncertainties from finite-size scaling. This will directly address the formal distinction between the averaged and conditioned ensembles while highlighting the numerical agreement we observe. revision: yes

Circularity Check

0 steps flagged

No circularity: transitions reported from independent simulations

full rationale

The paper derives the ballistic-diffusive transition from direct numerical simulation of the unconditioned Lindblad dynamics on the domain-wall initial state and the entanglement transition from postselected trajectories. The claim of interlinkage is presented as an observation from these separate computations plus theoretical arguments, not as a definitional equivalence, a fitted parameter renamed as prediction, or a result forced by self-citation. No load-bearing step reduces to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; insufficient information available.

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discussion (0)

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Reference graph

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