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arxiv: 2507.11957 · v2 · pith:2NGJ3V5Knew · submitted 2025-07-16 · 🪐 quant-ph · cond-mat.dis-nn· cond-mat.stat-mech

Measurement-Induced Phase Transition in a Disordered XX Spin Chain: A Real-Space Renormalization Group Study

Siddharth Tiwary , Joel E. Moore This is my paper

Pith reviewed 2026-05-22 00:18 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.dis-nncond-mat.stat-mech
keywords measurement-induced phase transitiondisordered spin chainreal-space renormalization groupnon-Hermitian systemsXX modelopen quantum systemsstochastic measurements
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The pith

Random measurements in disordered XX spin chains produce new strongly disordered fixed points through non-unitary dynamics.

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

This paper examines the disordered XX spin chain under stochastic local measurements in the X and Y bases. It maps the open system to a non-Hermitian spin ladder with complex couplings and applies an RSRG-X renormalization procedure to the resulting effective model. The calculation identifies a new class of strongly disordered fixed points generated specifically by the non-unitary contributions. A reader would care because the result shows how measurement-induced non-Hermiticity enlarges the set of critical behaviors that real-space renormalization can reach in disordered quantum chains.

Core claim

The monitored disordered XX chain, after mapping to a non-Hermitian spin ladder with complex couplings, flows under RSRG-X to a new class of strongly disordered fixed points that arise directly from the non-unitary character of the measurements.

What carries the argument

Mapping the monitored XX chain with stochastic local measurements to a non-Hermitian spin ladder with complex couplings, enabling RSRG-X analysis of the open-system fixed points.

If this is right

  • Non-unitary effects from measurements generate fixed-point structures unavailable in purely unitary disordered spin chains.
  • The RSRG-X method becomes applicable to a broader range of open quantum systems with both disorder and monitoring.
  • Critical exponents and scaling near these fixed points differ from those of the standard Hermitian RSRG fixed points.
  • The landscape of possible phases in monitored many-body systems expands to include new strongly disordered regimes.

Where Pith is reading between the lines

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

  • Similar non-unitary fixed points may appear in other monitored spin models such as the Ising chain under local measurements.
  • The approach could be extended to study measurement-induced transitions in two-dimensional lattices by generalizing the ladder mapping.
  • Quantum simulator experiments with tunable disorder and mid-circuit measurements could directly probe the predicted flow to infinite disorder.

Load-bearing premise

The mapping from the monitored XX chain with stochastic local measurements to a non-Hermitian spin ladder with complex couplings preserves the essential physics needed for the RSRG-X flow.

What would settle it

Direct numerical simulation of the monitored disordered XX chain that checks whether the effective disorder strength grows without bound under repeated measurements in the manner predicted by the RSRG-X fixed-point analysis.

Figures

Figures reproduced from arXiv: 2507.11957 by Joel E. Moore, Siddharth Tiwary.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
read the original abstract

Spin chains with quenched disorder exhibit rich critical behavior, often captured by real-space renormalization group (RSRG) techniques. However, the physics of such systems in the presence of random measurements (i.e., non-Hermitian dephasing) remains largely unexplored. The interplay between measurements and unitary dynamics gives rise to novel phases and phase transitions in monitored quantum systems. In this work, we investigate the disordered XX spin chain subject to stochastic local measurements in the $X$ and $Y$ bases. By mapping the monitored chain to a non-Hermitian spin ladder with complex couplings, we propose an RSRG-for-excited-states (RSRG-X) approach for this open-system setting. Our analysis reveals a new class of strongly disordered fixed points that emerge due to non-unitarity, broadening the landscape of critical phenomena accessible via RSRG.

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 manuscript investigates the disordered XX spin chain subject to stochastic local measurements in the X and Y bases. By mapping the monitored system to a non-Hermitian spin ladder with complex couplings, the authors extend the RSRG-for-excited-states (RSRG-X) method to this open-system setting and report a new class of strongly disordered fixed points that arise due to non-unitarity.

Significance. If the mapping is faithful and the RSRG-X analysis with complex couplings is rigorously controlled, the work would extend real-space renormalization techniques beyond Hermitian disordered systems and identify novel measurement-induced critical phenomena, thereby broadening the landscape of accessible fixed points in monitored quantum spin chains.

major comments (2)
  1. [Mapping to non-Hermitian ladder (likely §2–3)] The central claim of new strongly disordered fixed points rests on the mapping of the monitored disordered XX chain (with random X/Y measurements) to a non-Hermitian spin ladder with complex couplings (abstract and the section introducing the effective model). The manuscript must explicitly derive how stochastic measurements translate into complex couplings while preserving the measurement-induced ensemble (trajectory averaging or post-selection) without introducing spurious decoherence or modifying the disorder distribution in a manner that alters the RG flow.
  2. [RSRG-X procedure and fixed-point analysis] Standard RSRG-X relies on Hermitian or real couplings for excited-state decimation. With complex couplings, non-real eigenvalues appear and decimation rules change; the paper needs to demonstrate that these altered rules remain stable under iterated RG steps and do not produce unphysical flows (the section applying RSRG-X to the ladder).
minor comments (2)
  1. Notation for the complex couplings and the disorder distribution in the effective ladder should be defined more explicitly to facilitate reproduction of the RG steps.
  2. Figure captions could more clearly indicate which fixed points correspond to the new non-unitary class versus previously known Hermitian ones.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript. We address each major comment below and outline the revisions we will make to strengthen the presentation and rigor of our results.

read point-by-point responses

  1. Referee: [Mapping to non-Hermitian ladder (likely §2–3)] The central claim of new strongly disordered fixed points rests on the mapping of the monitored disordered XX chain (with random X/Y measurements) to a non-Hermitian spin ladder with complex couplings (abstract and the section introducing the effective model). The manuscript must explicitly derive how stochastic measurements translate into complex couplings while preserving the measurement-induced ensemble (trajectory averaging or post-selection) without introducing spurious decoherence or modifying the disorder distribution in a manner that alters the RG flow.

    Authors: We agree that an explicit derivation is essential for clarity. In the revised manuscript we will expand Section 2 with a step-by-step derivation showing how the stochastic projective measurements in the X and Y bases generate the complex on-site and inter-leg couplings of the effective non-Hermitian ladder. We will explicitly demonstrate that the mapping is performed at the level of individual trajectories (post-selection) and that ensemble averaging over measurement outcomes reproduces the original disorder distribution without additional decoherence channels. This ensures the RG flow remains faithful to the monitored dynamics. revision: yes

  2. Referee: [RSRG-X procedure and fixed-point analysis] Standard RSRG-X relies on Hermitian or real couplings for excited-state decimation. With complex couplings, non-real eigenvalues appear and decimation rules change; the paper needs to demonstrate that these altered rules remain stable under iterated RG steps and do not produce unphysical flows (the section applying RSRG-X to the ladder).

    Authors: We have examined the modified decimation rules for complex couplings in our RSRG-X implementation. The manuscript already contains analytic expressions for the renormalized couplings that incorporate both real and imaginary parts, together with numerical evidence that the flow converges to the reported strongly disordered fixed points without runaway imaginary components. In the revision we will add an appendix with explicit iteration examples and a stability analysis showing that the imaginary parts remain bounded and do not induce unphysical divergences under repeated RG steps. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation relies on proposed mapping and RSRG-X extension

full rationale

The paper's central result follows from proposing a mapping of the monitored disordered XX chain to a non-Hermitian spin ladder, then applying an RSRG-X procedure to identify new fixed points induced by non-unitarity. This mapping and subsequent RG analysis are presented as an extension of existing techniques rather than a self-referential definition, fitted parameter renamed as prediction, or load-bearing self-citation chain. No equations reduce by construction to their inputs, and the derivation chain remains independent of the target claims. The abstract and described approach contain no evidence of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests primarily on the validity of mapping the stochastic measurement process to a non-Hermitian ladder and the applicability of the RSRG-X technique to capture non-unitary effects in the disordered setting.

axioms (1)
  • domain assumption The monitored chain with random X and Y measurements can be mapped to a non-Hermitian spin ladder with complex couplings while preserving the critical physics.
    This mapping is the foundational step proposed to enable the RSRG-X analysis.

pith-pipeline@v0.9.0 · 5688 in / 1230 out tokens · 46241 ms · 2026-05-22T00:18:08.391775+00:00 · methodology

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Reference graph

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    Decimating Ji The rules for when a type-0 cell is decimated were de- rived in the main text. Here, we look at the rules for decimating cell of types1, 2, 3, and 4. For cells of types1, 2, 3, and 4, respectively, the un- perturbed bit is L(1) 0 = Ji[(Xixi+1 + Yiyi+1) + (xiXi+1 + yiYi+1) − (XiXi+1 + YiYi+1) − (xixi+1 + yiyi+1)], L(2) 0 = Ji[(Xixi+1 + Yiyi+1...

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  64. [64]

    The star(∗) indicates complex conjugation

    Decimating pi/2 Here, Lvert 0 = pi 2 [(Xixi + Yiyi) − 2I] , (A4) while Lvert pert = Gi(XiXi+1 + YiYi+1) + G∗ i (xixi+1 + yiyi+1) + Hi(Xixi+1 + Yiyi+1) + H ∗ i (xiXi+1 + yiYi+1) + Gi−1(XiXi−1 + YiYi−1) + G∗ i−1(xixi−1 + yiyi−1) + Hi−1(Xi−1xi + Yi−1yi) + H ∗ i−1(Xixi−1 + Yiyi−1), (A5) with Gi, Hi ∈ {±Ji, ±iJi}, depending on the types of the cells adjacent t...

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