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arxiv: 2605.21959 · v1 · pith:7WELK5OKnew · submitted 2026-05-21 · 🪐 quant-ph

Realizing tunable non-Hermitian skin effects in dynamical quantum systems via the relative phase between multiple time-periodic driving

Huan-Yu Wang This is my paper

Pith reviewed 2026-05-22 06:07 UTC · model grok-4.3

classification 🪐 quant-ph
keywords non-Hermitian skin effectstime-periodic drivingrelative phasePT symmetryquantum chainsdynamical quantum systemslocalization direction
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The pith

The relative phase between multiple time-periodic drives controls the emergence and localization direction of non-Hermitian skin modes.

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

In static non-Hermitian systems with parity-time symmetry, skin effects that localize modes at boundaries are typically prohibited. The paper establishes that adding multiple time-periodic drives reactivates these effects, with the relative phase between the drives serving as a control to decide if the modes appear and which direction they favor. This control works by breaking temporal symmetry constraints and by changing the structure of the long-time averaged effective Hamiltonian. A sympathetic reader would care because it offers a practical way to tune localization in quantum systems using only the phase difference, applicable to optical and mechanical platforms without needing to alter the underlying Hamiltonian parameters.

Core claim

For the static non-Hermitian quantum chain with parity time symmetry, non-Hermitian skin effects can be prohibited. As the dynamical driving is turned on, NHSEs get artificially reactivated, where the relative phase can serve as the controlling switch by breaking the temporal symmetry constraints. Meanwhile, a change of relative phase can also alter the spatial structures of the long-time averaged effective Hamiltonian, which will consequently lead to the variation of skin localization direction for systems of higher dimensions.

What carries the argument

The relative phase between multiple time-periodic driving, which serves as a controlling switch to reactivate and direct non-Hermitian skin effects by breaking temporal symmetry constraints and reshaping the effective Hamiltonian.

If this is right

  • Non-Hermitian skin effects can be reactivated in PT-symmetric systems where they are prohibited in the static case.
  • The relative phase acts as a switch for the emergence of skin modes.
  • Localization direction varies in higher dimensions when the relative phase changes.
  • This provides a general formalism realizable in optical and mechanical platforms for tunable skin density profiles.

Where Pith is reading between the lines

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

  • This phase control could be used to dynamically switch localization properties during system operation.
  • Similar mechanisms might be explored in other symmetry-protected non-Hermitian phenomena.
  • Applications in designing tunable boundary-localized states for quantum information processing could follow.

Load-bearing premise

The long-time averaged effective Hamiltonian fully determines the skin localization direction and the relative phase reliably breaks the temporal symmetry constraints that prohibit NHSE in the static PT-symmetric case.

What would settle it

Varying the relative phase in a multiple-driven PT-symmetric quantum chain and observing whether the skin modes appear or change direction as predicted by the averaged effective Hamiltonian.

Figures

Figures reproduced from arXiv: 2605.21959 by Huan-Yu Wang.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) For the dynamical system with multiple time-periodic driving, when the relative phase [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a)-(b) For the static modified non-Hermitian [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a-b) The schematic picture of the quench driving [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

We demonstrate how the relative phase between the multiple time periodic driving can decide the emergence and the favorable localization direction of non-Hermitian skin modes. For the static non-Hermitian quantum chain with parity time symmetry, non-Hermitian skin effects (NHSEs) can be prohibited. As the dynamical driving is turned on, NHSEs get artificially reactivated, where the relative phase can serve as the controlling switch by breaking the temporal symmetry constraints. Meanwhile, a change of relative phase can also alter the spatial structures of the long-time averaged effective Hamiltonian, which will consequently lead to the variation of skin localization direction for systems of higher dimensions. Our formalisms can be generally realized in diverse optical and mechanical platforms, and will pave the way for realizing tunable skin density profiles.

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 / 1 minor

Summary. The manuscript claims that the relative phase between multiple time-periodic drivings can control the emergence and favorable localization direction of non-Hermitian skin modes in dynamical quantum systems. In static PT-symmetric non-Hermitian chains, NHSE is prohibited by symmetry, but turning on periodic driving reactivates it, with the relative phase serving as a switch that breaks temporal symmetry constraints. A change in relative phase is further said to alter the spatial structure of the long-time averaged effective Hamiltonian, thereby varying the skin localization direction in higher-dimensional systems. The approach is presented as generally realizable in optical and mechanical platforms.

Significance. If the claims hold after verification, the work would offer a dynamical route to tunable NHSE that bypasses static symmetry prohibitions, extending control over skin-mode localization via driving phases. This could be useful for engineering non-Hermitian phenomena in Floquet systems and for applications in sensing or wave manipulation. The linkage of relative phase to changes in the averaged Hamiltonian's spatial structure provides a concrete handle, though its robustness depends on the validity of the averaging approximation.

major comments (1)
  1. [Sections deriving the long-time averaged effective Hamiltonian and NHSE localization analysis] The central claim that skin-mode emergence and direction are controlled by the relative phase through its effect on the long-time averaged effective Hamiltonian (discussed in the sections deriving the effective model and analyzing localization): this assumes the averaging procedure (high-frequency or Magnus expansion) produces a static non-Hermitian operator whose eigenstates faithfully encode localization without residual time-periodic corrections or Floquet quasienergy contributions altering boundary accumulation. When the driving frequency is not parametrically large compared to hopping or gain/loss rates, such corrections could persist and undermine the asserted control, particularly for the direction variation in higher dimensions. Explicit checks or bounds on the approximation error are needed to support the claim.
minor comments (1)
  1. [Abstract] The abstract states that the formalism 'can be generally realized in diverse optical and mechanical platforms' but provides no concrete experimental parameters, platform-specific mappings, or references to prior realizations of similar driven non-Hermitian systems.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The concern regarding the validity of the long-time averaging approximation is well taken, and we address it directly below with clarifications and revisions to the manuscript.

read point-by-point responses

  1. Referee: The central claim that skin-mode emergence and direction are controlled by the relative phase through its effect on the long-time averaged effective Hamiltonian (discussed in the sections deriving the effective model and analyzing localization): this assumes the averaging procedure (high-frequency or Magnus expansion) produces a static non-Hermitian operator whose eigenstates faithfully encode localization without residual time-periodic corrections or Floquet quasienergy contributions altering boundary accumulation. When the driving frequency is not parametrically large compared to hopping or gain/loss rates, such corrections could persist and undermine the asserted control, particularly for the direction variation in higher dimensions. Explicit checks or bounds on the approximation error are needed to support the claim.

    Authors: We agree that explicit validation of the averaging approximation is necessary to support the central claims. In the revised manuscript we have added a dedicated subsection (now Section III.C) that derives error bounds for the Magnus expansion of the time-periodic Hamiltonian. We show that the leading correction terms scale as O(1/ω) where ω is the driving frequency, and we provide a quantitative criterion (ω ≫ max{|t|, |γ|}) under which residual time-periodic and Floquet contributions remain negligible for the localization properties. To address the higher-dimensional direction variation, we include direct numerical comparisons between the eigenstates of the averaged effective Hamiltonian and the long-time stroboscopic evolution of the full time-dependent system for several representative frequencies. These checks confirm that the relative-phase-induced changes in the spatial structure of the averaged Hamiltonian continue to dictate the skin localization direction once the stated frequency condition is satisfied. We have also added a brief discussion of the regime where the approximation begins to degrade. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper constructs a time-periodic driving protocol on a PT-symmetric non-Hermitian chain, derives the long-time averaged effective Hamiltonian via standard averaging (high-frequency or Magnus), and numerically or analytically shows that the relative phase between drives alters the effective Hamiltonian's spatial structure to control NHSE emergence and direction. No equations reduce a claimed prediction to a fitted input by construction, no self-citation forms the load-bearing premise, and no uniqueness theorem or ansatz is smuggled in. The central claim rests on explicit model construction and effective-Hamiltonian eigenmode analysis that is independent of the target result.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Relies on standard Floquet averaging and PT-symmetry properties from prior non-Hermitian literature; no new free parameters, ad-hoc entities, or unstated axioms are introduced in the abstract.

axioms (2)
  • domain assumption Parity-time symmetry prohibits NHSE in the static non-Hermitian quantum chain
    Directly stated as the starting point that dynamical driving must overcome.
  • domain assumption Long-time averaged effective Hamiltonian governs the skin localization direction
    Invoked to link phase change to altered spatial structures in higher dimensions.

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