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arxiv: 2604.05850 · v1 · submitted 2026-04-07 · ❄️ cond-mat.stat-mech · quant-ph

Recognition: 2 theorem links

· Lean Theorem

Generalized hydrodynamics of free fermions under extensive-charge monitoring

Pablo Bayona-Pena , Michele Mazzoni , Lorenzo Piroli
Authors on Pith no claims yet

Pith reviewed 2026-05-10 18:45 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech quant-ph
keywords generalized hydrodynamicsfree fermionsquantum monitoringZeno limittransportquench dynamicsLindblad dynamicsdomain wall
0
0 comments X

The pith

Monitoring the particle number in half a free-fermion chain reduces to localized impurities in the hydrodynamic description and suppresses all transport at infinite monitoring rate.

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

The paper shows that continuous monitoring of total particle number over one half of a free-fermion system, although described by a non-local Lindbladian, produces density and current profiles that can be captured by adding simple localized impurities to the generalized hydrodynamics equations. This reduction yields a hybrid method that solves large-scale quench dynamics analytically where possible and numerically otherwise. For domain-wall initial conditions the impurities create jumps in the local observables whose magnitude grows with monitoring strength, and these jumps grow large enough to eliminate net particle flow when the monitoring rate diverges.

Core claim

Within the generalized hydrodynamics picture the non-local averaged dynamics generated by extensive charge monitoring on free fermions is equivalent to the insertion of localized impurities at the boundary of the monitored region. Domain-wall quenches then develop discontinuous profiles in density and current; the size of the discontinuities increases with monitoring rate and reaches full suppression of transport in the Zeno limit of infinite rate.

What carries the argument

Localized impurities inserted into the generalized hydrodynamics (GHD) equations to replace the non-local Lindbladian for bipartition monitoring protocols.

If this is right

  • Density and current profiles acquire discontinuities whose size grows with monitoring rate.
  • Net transport vanishes completely in the Zeno limit of infinite monitoring rate.
  • The GHD framework supplies a hybrid numerical-analytic route to quench dynamics at hydrodynamic scales.
  • The same impurity construction extends directly to interacting integrable models.

Where Pith is reading between the lines

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

  • The impurity reduction may apply to other extensive monitoring schemes that preserve integrability.
  • In the Zeno limit the two halves effectively decouple with conserved particle numbers in each.
  • Interactions could alter the functional dependence of discontinuity size on monitoring rate.

Load-bearing premise

The effects of the non-local Lindbladian for averaged dynamics can be replaced by localized impurities inside the GHD description for the bipartition and domain-wall protocols considered.

What would settle it

Exact numerical integration of the full Lindblad master equation on chains of several hundred sites that shows whether the hydrodynamic density and current profiles develop the predicted discontinuities or remain smooth at the monitoring boundary.

Figures

Figures reproduced from arXiv: 2604.05850 by Lorenzo Piroli, Michele Mazzoni, Pablo Bayona-Pena.

Figure 1
Figure 1. Figure 1: Pictorial representation of the monitoring protocol studied in this work. The [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: a) Non-unitary dynamics of the charge ⟨qˆ (0,+) x (t)⟩. The system is prepared in a domain-wall state given by Eq. (38). A light cone due to ballistic propagation of quasi￾particles is present with front at ζ ∗ = ±max(|v(k)|) = ±2J. b) Late time profile of the local charge ⟨qˆ (0,+) x (t)⟩ for ζ = x/t. Far from the propagation front ray ζ ∗ , the charge profile remains constant, while it displays a discont… view at source ↗
Figure 3
Figure 3. Figure 3: Values of the local charges in the NESS. The plots only show the charges that [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Local charge and current density profiles at late times for the initial domain-wall [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Upper panel: Root density profile for different cutoff values [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Charge and current profiles at the hydrodynamic scale for an initial homogeneous [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Charge and current profiles at the hydrodynamic scale for an initial homogeneous [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Local charge and current density profiles at late times for the initial domain-wall [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Local charge and current density profiles at late times for the initial homogeneous [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Local charge and current density profiles at late times for the initial fully [PITH_FULL_IMAGE:figures/full_fig_p024_10.png] view at source ↗
read the original abstract

We study transport dynamics of free fermions subject to the external monitoring of a conserved charge over an extensive region. Focusing on bipartition protocols, we consider monitoring the total particle number over half of the system, and study the profiles of local charges and currents at hydrodynamic scales. While the Lindbladian describing the averaged dynamics is non-local, we show that the profiles can be understood in terms of localized impurities. We present a general framework based on the generalized hydrodynamics (GHD) picture, allowing for a hybrid numerical-analytic solution of the quench dynamics at hydrodynamic scales. We illustrate our approach for domain-wall initial states, showing that monitoring leads to discontinuities in the profiles that become more pronounced as the rate increases and that lead to the absence of transport in the Zeno limit of infinite monitoring rates. Our GHD framework could be naturally extended to interacting systems, paving the way for a systematic study of transport of integrable models subject to extensive-charge measurements.

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 develops a generalized hydrodynamics (GHD) framework for the hydrodynamic-scale quench dynamics of free fermions under extensive charge monitoring in bipartition protocols. It maps the non-local Lindbladian (arising from monitoring total particle number over half the system) onto an effective description in terms of localized impurities, enabling a hybrid analytic-numerical solution. For domain-wall initial states, the approach predicts discontinuities in local charge and current profiles that grow with monitoring rate and produce vanishing transport in the Zeno limit of infinite rate. The framework is presented as extensible to interacting integrable models.

Significance. If the impurity mapping is rigorously justified, the work supplies a concrete route to hydrodynamic predictions for monitored free-fermion systems and a template for monitored integrable models more generally. The hybrid solution method and the explicit Zeno-limit result constitute genuine technical contributions that could be reused in related settings.

major comments (2)
  1. [Section describing the impurity mapping (around the transition from Lindbladian to GHD)] The central technical step—reduction of the non-local Lindbladian to a localized impurity within the GHD quasiparticle picture—is load-bearing for every subsequent claim (discontinuities, rate dependence, Zeno limit). No explicit formula is supplied that relates the monitoring rate γ to the impurity scattering phase shift (or equivalent GHD boundary condition) for the bipartition geometry. Without this relation, it is impossible to verify that all non-local contributions are captured by a single local defect rather than residual long-range terms.
  2. [Section on domain-wall results and Zeno limit] The hybrid numerical-analytic solution for domain-wall quenches relies on the above mapping to set the effective boundary condition. Because the mapping lacks a first-principles derivation, the reported profiles and the statement that transport vanishes in the Zeno limit rest on an unverified effective model; numerical illustrations alone do not establish completeness of the reduction.
minor comments (2)
  1. Notation for the monitoring operator and the GHD rapidity variable should be introduced once and used consistently; occasional redefinition of symbols across sections slows reading.
  2. [Conclusion] The abstract states that the framework 'could be naturally extended to interacting systems,' but the manuscript contains no concrete indication of how the impurity mapping would generalize beyond free fermions; a brief remark on the obstacles would be useful.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading, positive assessment of the work's potential significance, and constructive comments. We address the major points below and will revise the manuscript accordingly to strengthen the presentation of the impurity mapping.

read point-by-point responses

  1. Referee: [Section describing the impurity mapping (around the transition from Lindbladian to GHD)] The central technical step—reduction of the non-local Lindbladian to a localized impurity within the GHD quasiparticle picture—is load-bearing for every subsequent claim (discontinuities, rate dependence, Zeno limit). No explicit formula is supplied that relates the monitoring rate γ to the impurity scattering phase shift (or equivalent GHD boundary condition) for the bipartition geometry. Without this relation, it is impossible to verify that all non-local contributions are captured by a single local defect rather than residual long-range terms.

    Authors: We agree that an explicit relation between the monitoring rate γ and the effective impurity scattering phase shift (or GHD boundary condition) is essential for rigorous verification of the mapping. The manuscript derives the reduction by analyzing the action of the non-local Lindbladian on the quasiparticle distribution functions within the GHD picture for the bipartition geometry, showing that it acts as a localized defect. However, to address this concern directly, the revised manuscript will include a detailed derivation of the explicit formula relating γ to the phase shift, demonstrating that all non-local contributions are captured by this single local defect in the hydrodynamic limit with no residual long-range terms. revision: yes

  2. Referee: [Section on domain-wall results and Zeno limit] The hybrid numerical-analytic solution for domain-wall quenches relies on the above mapping to set the effective boundary condition. Because the mapping lacks a first-principles derivation, the reported profiles and the statement that transport vanishes in the Zeno limit rest on an unverified effective model; numerical illustrations alone do not establish completeness of the reduction.

    Authors: We acknowledge that the hybrid solution and the Zeno-limit claim depend on the mapping. With the addition of the explicit γ-dependent phase-shift formula and first-principles derivation in the revision (as outlined above), the boundary condition will be placed on a rigorous footing. The numerical illustrations demonstrate the resulting profiles and the suppression of transport; in the revised text we will clarify that the completeness of the reduction follows from the derived local defect, and provide an analytic argument for the Zeno limit in which infinite γ corresponds to a boundary condition that enforces vanishing current. revision: yes

Circularity Check

0 steps flagged

No circularity: GHD framework applied to monitoring without reduction to fitted inputs or self-citations

full rationale

The paper derives profiles from the non-local Lindbladian by mapping to localized impurities in the GHD quasiparticle picture for bipartition and domain-wall setups. This mapping is presented as a derived effective description allowing hybrid analytic-numerical solution, not as a fit to the target profiles or a renaming of known results. No equations reduce the discontinuity heights or Zeno-limit vanishing transport to quantities defined from the same data by construction. The approach extends standard GHD without load-bearing self-citation chains or ansatz smuggling; numerical illustrations are consistent with but not constitutive of the central claim. The derivation chain remains self-contained against external GHD benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The monitoring rate is the principal free parameter. The framework rests on standard domain assumptions about Lindblad-averaged dynamics and the validity of GHD at hydrodynamic scales; no new entities are postulated.

free parameters (1)
  • monitoring rate
    Parameter controlling monitoring strength, varied across regimes including the Zeno limit.
axioms (2)
  • domain assumption Averaged dynamics under continuous monitoring obey a Lindblad master equation
    Standard assumption for open quantum systems invoked to describe the non-local monitoring.
  • domain assumption Generalized hydrodynamics applies to the effective large-scale description
    The paper relies on the GHD picture to obtain profiles and currents.

pith-pipeline@v0.9.0 · 5462 in / 1529 out tokens · 53999 ms · 2026-05-10T18:45:40.097796+00:00 · methodology

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Reference graph

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