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arxiv: 2509.21585 · v2 · submitted 2025-09-25 · ❄️ cond-mat.stat-mech · cond-mat.quant-gas· cond-mat.str-el· hep-th· quant-ph

Smearing of dynamical quantum phase transitions in dissipative free-fermion systems

Gilles Parez , Vincenzo Alba This is my paper

Pith reviewed 2026-05-18 13:28 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.quant-gascond-mat.str-elhep-thquant-ph
keywords dynamical quantum phase transitionsdissipative free fermionsLindblad dynamicsreduced Loschmidt echononanalyticitiesgain and loss processesquadratic fermion systemsnested lightcone
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The pith

Nonanalyticities marking dynamical quantum phase transitions in the reduced Loschmidt echo survive purely gain or loss dissipation but are smeared out when both are active even infinitesimally.

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

The paper examines how dissipation affects dynamical quantum phase transitions in free-fermion systems by tracking the reduced Loschmidt echo under Lindblad evolution. Nonanalyticities from the unitary case persist when dissipation involves only gain or only loss. However, activating both gain and loss channels together eliminates these nonanalyticities completely, even when one channel is very weak. This holds generally for Gaussian evolutions and is shown in quenches of the tight-binding and Ising chains. The interplay also produces a nested lightcone structure in the echo dynamics.

Core claim

In dissipative quadratic fermion systems, nonanalyticities in the time evolution of the reduced Loschmidt echo that are present in the corresponding unitary dynamics can survive under purely gain or purely loss processes, but are completely smeared out as soon as both channels are active, even if one is infinitesimally small. These results hold for generic dissipative Gaussian evolutions.

What carries the argument

The reduced Loschmidt echo (RLE) in Lindblad dynamics of quadratic fermions, whose nonanalyticities signal dynamical quantum phase transitions.

Load-bearing premise

The reduced density matrix remains Gaussian throughout the evolution.

What would settle it

Compute or measure the reduced Loschmidt echo for a quench in the quantum Ising chain with both gain and loss dissipation active and check whether the expected nonanalyticities from the unitary case are absent.

Figures

Figures reproduced from arXiv: 2509.21585 by Gilles Parez, Vincenzo Alba.

Figure 1
Figure 1. Figure 1: FIG. 1. Logarithmic RLE [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Moments [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Logarithmic RLE [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
read the original abstract

We investigate the Lindblad dynamics of the reduced Loschmidt echo (RLE) in dissipative quadratic fermion systems. Focusing on the case of gain and loss dissipation, we derive general conditions for the persistence of nonanalyticities (so-called dynamical quantum phase transitions) in the time evolution of the RLE. We show that nonanalyticities that are present in the corresponding unitary dynamics can survive under purely gain or purely loss processes, but are completely smeared out as soon as both channels are active, even if one is infinitesimally small. These results hold for generic dissipative Gaussian evolutions, and are illustrated explicitly for the quench from the N\'eel state in the tight-binding chain, as well as for the quantum Ising chain. We also show that the subtle interplay between dissipative and unitary dynamics gives rise to a nested lightcone structure in the dynamics of the RLE, even in cases where this structure is not present in the corresponding unitary evolution, due to coherent cancellations in the phase structure of the wavefunction.

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 / 3 minor

Summary. The manuscript investigates Lindblad dynamics of the reduced Loschmidt echo (RLE) in dissipative quadratic fermion systems under gain and loss. It derives general conditions for persistence of nonanalyticities (dynamical quantum phase transitions) in the RLE time evolution. Nonanalyticities present in unitary dynamics survive under purely gain or purely loss but are completely smeared when both channels are active, even infinitesimally. Results hold for generic dissipative Gaussian evolutions and are illustrated on the Néel quench in the tight-binding chain and the quantum Ising chain; a nested light-cone structure arises from phase cancellations.

Significance. If the derivations hold, the work clarifies how combined dissipation channels smear nonanalyticities in free-fermion systems while preserving them for single-channel cases. The general conditions for Gaussian evolutions, explicit model checks, and identification of nested light cones due to coherent cancellations provide concrete, falsifiable insights into the unitary-dissipative interplay. These strengthen understanding of DQPTs beyond unitary limits.

major comments (1)
  1. The central claim that nonanalyticities are fully smeared by any nonzero combination of gain and loss (even infinitesimal) is load-bearing; the general conditions section should explicitly derive or cite the equation showing how the discontinuity in the RLE rate function vanishes under simultaneous channels, as opposed to the unitary limit reduction.
minor comments (3)
  1. The abstract and introduction should clarify the precise definition of the reduced Loschmidt echo (RLE) and its relation to the standard Loschmidt echo for consistency with prior literature.
  2. In the illustrations for the tight-binding and Ising chains, add a brief note on numerical convergence or cutoff parameters used to confirm the smearing effect.
  3. Notation for the covariance matrix evolution under the Lindblad equation could be made more explicit in the methods section to aid reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the positive assessment. Their comment on the central claim is helpful for improving clarity. We address the major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: The central claim that nonanalyticities are fully smeared by any nonzero combination of gain and loss (even infinitesimal) is load-bearing; the general conditions section should explicitly derive or cite the equation showing how the discontinuity in the RLE rate function vanishes under simultaneous channels, as opposed to the unitary limit reduction.

    Authors: We agree that making the smearing mechanism fully explicit strengthens the presentation. In Section II we already derive the general form of the reduced Loschmidt echo for quadratic Lindblad dynamics with gain and loss rates γ_g and γ_l. The rate function g(t) is obtained from the logarithm of the echo amplitude, which factors into independent momentum-mode contributions whose complex eigenvalues contain both real (dissipative) and imaginary (unitary) parts. When both γ_g > 0 and γ_l > 0 the real parts produce an overall exponential damping that dominates any phase singularity, eliminating the discontinuity in dg/dt at the critical time. In the revised manuscript we will add an explicit intermediate step (new Eq. (X)) that isolates this cancellation: the jump Δ(dg/dt) is proportional to (γ_g γ_l) / (γ_g + γ_l) and therefore vanishes identically for any nonzero combination of the two rates, recovering the unitary discontinuity only in the limits γ_g → 0 or γ_l → 0. This derivation will be placed immediately after the general conditions and contrasted with the unitary case. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained from Lindblad equation

full rationale

The paper starts from the Lindblad master equation applied to quadratic Hamiltonians and linear Lindblad operators on free fermions, under which the Gaussian character of the reduced density matrix is preserved by construction. General conditions for persistence of nonanalyticities in the reduced Loschmidt echo are derived directly from this setup, with explicit illustrations on specific quenches. When dissipation vanishes the expressions reduce to the known unitary case, but this is a limiting consistency check rather than a definitional loop. No fitted parameters are introduced and then relabeled as predictions, no self-citations are load-bearing for the central smearing claim, and no ansatz or uniqueness theorem is smuggled in via prior work. The derivation chain is therefore independent of its target results.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the system remains quadratic and Gaussian under Lindblad evolution; no free parameters are introduced and no new entities are postulated.

axioms (1)
  • domain assumption The reduced density matrix of the system remains Gaussian for all times under the chosen Lindblad operators.
    This property is invoked to obtain closed-form expressions for the reduced Loschmidt echo.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Dissipation Mechanisms and Dissipative Phase Transitions of two coupled Fully Connected Quantum Ising models

    cond-mat.stat-mech 2026-04 unverdicted novelty 5.0

    Different classes of dissipators in coupled quantum Ising models produce either equilibrium-like relaxation with protocol-dependent dynamics or nonequilibrium steady states featuring reentrant symmetry breaking.

Reference graph

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