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arxiv: 2605.15982 · v2 · pith:6I2MMM6Mnew · submitted 2026-05-15 · 🪐 quant-ph

Biorthogonal dynamical quantum phase transitions in non-Hermitian topological superconductors

Haoran Gu , Yubo Zhao , Siyuan Cheng , Yuee Xie , Xiaosen Yang , Yuanping Chen This is my paper

Pith reviewed 2026-06-30 19:31 UTC · model grok-4.3

classification 🪐 quant-ph
keywords dynamical quantum phase transitionsnon-Hermitian systemstopological superconductorsKitaev chainbiorthogonal formalismLoschmidt rate functionFisher zeros
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The pith

A biorthogonal associated-state formalism shifts the critical times of dynamical quantum phase transitions in non-Hermitian topological superconductors.

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

Non-Hermitian systems feature eigenstates that are biorthogonal rather than orthogonal, which complicates the definition of dynamical quantities such as the Loschmidt echo. This paper applies an associated-state formalism to the non-Hermitian Kitaev chain, a model of topological superconductors, and uses it to rewrite the Loschmidt rate function, dynamical topological order parameter, and dynamical Fisher zeros. The reformulation produces critical times for dynamical quantum phase transitions that differ from those obtained with conventional self-normalized methods. Momentum-resolved analysis at critical momenta confirms the framework remains consistent. The work shows that biorthogonality must be built into nonequilibrium descriptions to obtain reliable transition points.

Core claim

Taking the non-Hermitian Kitaev chain as a prototypical model, we construct an associated-state formalism and reformulate the Loschmidt rate function, dynamical topological order parameter, and dynamical Fisher zeros. Within this framework, the critical times at which dynamical quantum phase transitions occur differ from those based on the conventional self-normal approaches.

What carries the argument

Associated-state formalism that incorporates the biorthogonal structure of non-Hermitian eigenstates into the Loschmidt rate function and dynamical order parameter.

If this is right

  • Critical times of dynamical quantum phase transitions are shifted relative to self-normal approaches.
  • Momentum-resolved subsystems at critical momenta remain well-defined under the biorthogonal reformulation.
  • The framework establishes a consistent description of nonequilibrium dynamics that respects biorthogonality.
  • Dynamical Fisher zeros and the dynamical topological order parameter acquire new locations when biorthogonality is enforced.

Where Pith is reading between the lines

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

  • The same associated-state construction could be tested on other non-Hermitian lattice models with different topological invariants.
  • Numerical simulations of finite-size chains could quantify how the shift in critical times scales with system size.
  • If realized in driven open systems, the shifted transitions would imply that topological protection of edge modes must be re-examined under biorthogonal time evolution.

Load-bearing premise

The associated-state formalism correctly captures the biorthogonal structure of the non-Hermitian eigenstates for the purpose of defining the Loschmidt rate function and dynamical order parameter.

What would settle it

An experiment on a physical non-Hermitian Kitaev chain that measures the times of dynamical quantum phase transitions and checks whether they match the biorthogonal predictions or the conventional self-normal predictions.

Figures

Figures reproduced from arXiv: 2605.15982 by Haoran Gu, Siyuan Cheng, Xiaosen Yang, Yuanping Chen, Yubo Zhao, Yuee Xie.

Figure 1
Figure 1. Figure 1: (a) also shows the conventional Loschmidt echo L(t) = |⟨Ψ(0)|Ψ(t)⟩|2 , together with an enforced nor￾malization factor [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_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (b) indicates that multiple critical momenta kc can exist, each associated with a distinct critical time tc. Moreover, a characteristic pattern is observed: for t < tc, p(kc, t) exhibits n local maxima and reaches 1 at the (n + 1)-th maximum, whereas for t ≫ tc, it tends to a steady state. By employing a biorthogonal framework, we study DQPTs in a non-Hermitian Kitaev chain. This formula￾tion applies to ge… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

Dynamical quantum phase transitions in non-Hermitian systems pose fundamental challenges due to the intrinsic biorthogonality of their eigenstates. In this work, we extend a biorthogonal framework to investigate dynamical quantum phase transitions in non-Hermitian topological superconductors. Taking the non-Hermitian Kitaev chain as a prototypical model, we construct an associated-state formalism and reformulate the Loschmidt rate function, dynamical topological order parameter, and dynamical Fisher zeros. Within this framework, we find that the critical times at which dynamical quantum phase transitions occur differ from those based on the conventional self-normal approaches. We further analyze momentum-resolved subsystems at critical momenta and demonstrate the robustness of the biorthogonal framework. Our work highlights the essential role of biorthogonality in nonequilibrium dynamics and establishes a consistent theoretical framework for dynamical quantum phase transitions in non-Hermitian topological superconductors.

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 / 0 minor

Summary. The manuscript extends a biorthogonal framework to dynamical quantum phase transitions (DQPTs) in non-Hermitian topological superconductors. Using the non-Hermitian Kitaev chain, it introduces an associated-state formalism to reformulate the Loschmidt rate function, dynamical topological order parameter, and dynamical Fisher zeros. The central claim is that the critical times for DQPTs differ from those obtained via conventional self-normalized approaches; the work also examines momentum-resolved subsystems at critical momenta and asserts robustness of the biorthogonal construction.

Significance. If the associated-state construction is shown to be the correct and unique extension of the Loschmidt echo that respects left/right eigenvector biorthogonality under non-unitary evolution, the result would establish a consistent theoretical framework for DQPTs in non-Hermitian topological systems and clarify the role of biorthogonality in nonequilibrium dynamics.

major comments (1)
  1. [Section 3] Section 3 (reformulation paragraph): the claim that the associated-state overlap ⟨φ|ψ(t)⟩ directly supplies the generating function for the Loschmidt rate function and dynamical order parameter requires explicit derivation showing that no additional phase or normalization factors arise from the non-unitary time evolution. Without this step, the reported shift in critical times relative to self-normal approaches cannot be confirmed as a necessary consequence of biorthogonality rather than a convention-dependent artifact.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for highlighting the need for an explicit derivation in Section 3. We address the comment below and will revise the manuscript to strengthen the presentation of the associated-state formalism.

read point-by-point responses

  1. Referee: [Section 3] Section 3 (reformulation paragraph): the claim that the associated-state overlap ⟨φ|ψ(t)⟩ directly supplies the generating function for the Loschmidt rate function and dynamical order parameter requires explicit derivation showing that no additional phase or normalization factors arise from the non-unitary time evolution. Without this step, the reported shift in critical times relative to self-normal approaches cannot be confirmed as a necessary consequence of biorthogonality rather than a convention-dependent artifact.

    Authors: We agree that an explicit step-by-step derivation is required to rule out extraneous phase or normalization contributions. In the revised manuscript we will expand the reformulation paragraph in Section 3 to derive the Loschmidt rate function directly from the biorthogonal overlap ⟨φ|ψ(t)⟩. Starting from the non-unitary time-evolution operator generated by the non-Hermitian Hamiltonian, we show that the left and right eigenvectors remain biorthogonal at all times and that the overlap enters the rate function without additional global phases or rescaling factors that would alter the locations of the dynamical Fisher zeros. This derivation confirms that the shift in critical times is a direct consequence of the biorthogonal construction rather than a convention-dependent artifact. The same expanded derivation will be used for the dynamical topological order parameter. revision: yes

Circularity Check

0 steps flagged

No circularity: associated-state formalism is an independent construction

full rationale

The paper constructs an associated-state formalism to reformulate the Loschmidt rate function, dynamical topological order parameter, and Fisher zeros in the biorthogonal non-Hermitian setting, then reports that critical times differ from conventional self-normal approaches. No equations, self-citations, or definitional steps are shown that reduce this difference to a tautology, a fitted parameter renamed as prediction, or a load-bearing self-citation chain. The framework is presented as an extension that encodes left/right eigenvector structure, with the reported shift in critical times functioning as a distinguishable output rather than an input by construction. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no identifiable free parameters, axioms, or invented entities; the biorthogonal framework is treated as an extension of prior work rather than a new postulate.

pith-pipeline@v0.9.1-grok · 5693 in / 1128 out tokens · 20627 ms · 2026-06-30T19:31:45.846177+00:00 · methodology

Review history (2 revisions) →

discussion (0)

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Forward citations

Cited by 3 Pith papers

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

  1. Dynamical Entanglement Phase Transitions in Holographic CFTs

    hep-th 2026-05 unverdicted novelty 7.0

    In large-central-charge holographic CFTs, post-quench mutual information organizes into six phases governed by conformal block dominance and D4 symmetry breaking to Z2 x Z2.

  2. Unified resonant-manifold framework for dynamical quantum phase transitions

    quant-ph 2026-05 unverdicted novelty 7.0

    A resonant-manifold framework unifies manifold and branch DQPTs by attributing them to resonances within the initial manifold and with a transitional manifold connected by low-order processes, shown in Z2 LGT quenches.

  3. Unified resonant-manifold framework for dynamical quantum phase transitions

    quant-ph 2026-05 unverdicted novelty 5.0

    A resonant-manifold framework unifies manifold and branch DQPTs by linking them to resonances within the initial manifold or a transitional manifold, with regularity tied to manifold multiplicity, shown in Z2 LGT quenches.

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