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arxiv: 2606.10585 · v1 · pith:MDQZ36FYnew · submitted 2026-06-09 · 🪐 quant-ph · cond-mat.dis-nn

Anomalous mobility edges and extended-localized transition in a quasiperiodic emitter-cavity array

H. T. Cui , H. Z. Shen , M. Qin , X. X. Yi This is my paper

Pith reviewed 2026-06-27 13:10 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.dis-nn
keywords quasiperiodic systemsmobility edgeslocalization transitionemitter-cavity arraysquantum bound statesdissipation effectsphase diagram
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The pith

Dissipation in quasiperiodic emitter-cavity arrays produces anomalous mobility edges by switching effective hopping between exponential decay and sinusoidal oscillation according to bound-state type.

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

The paper shows that dissipation induces anomalous mobility edges and an extended-to-localized transition in arrays of emitters coupled to cavities under quasiperiodic potentials. Localization of the emitters is controlled by whether the underlying quantum bound states are discrete or embedded in the continuum, which in turn sets the form of the effective excitation hopping. Discrete bound states produce exponentially decaying hopping and therefore localized states, while continuum-embedded bound states produce sinusoidally oscillating hopping and therefore critical states. A generalized duality transformation supplies exact expressions for the mobility edges and the critical potential strength, yielding a complete phase diagram. The work concludes that cavity parameters alone can be used to tune excitation localization.

Core claim

The localization properties of emitters is governed by the nature of quantum bound states, either discrete or embedded in continuum, providing a unified mechanism linking the emitter-photon bound physics to quasiperiodic criticality. Depending on the bound state discrete or continuumlike, the induced effective excitation hopping exhibits either exponentially decaying or sinusoidally oscillating, giving rise to the formation of localized or critical states, respectively. Through a generalized duality transformation, the anomalous mobility edges and the critical strength of potential are determined analytically, enabling the construction of a full phase diagram. The physical characteristics of

What carries the argument

Effective excitation hopping whose functional form (exponentially decaying or sinusoidally oscillating) is dictated by whether the quantum bound state is discrete or continuum-embedded.

If this is right

  • Anomalous mobility edges appear whose locations are fixed by the duality transformation.
  • An extended-localized transition occurs at a critical potential strength that can be calculated exactly.
  • The full phase diagram in the plane of potential strength and cavity parameters is obtainable analytically.
  • Excitation localization can be switched on or off by tuning only the cavity fields while the quasiperiodic potential is held fixed.

Where Pith is reading between the lines

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

  • The same bound-state mechanism could be tested in other open quantum systems where dissipation couples to a quasiperiodic background.
  • Cavity tuning might offer an experimental knob for realizing mobility-edge physics in superconducting-circuit or trapped-ion arrays without changing the underlying lattice potential.
  • If the mapping from bound-state type to hopping form survives weak interactions, the construction would extend to many-body localization problems in driven cavity arrays.

Load-bearing premise

The effective excitation hopping remains strictly exponentially decaying for discrete bound states and sinusoidally oscillating for continuum-embedded bound states, with this form directly determining localized versus critical behavior without further corrections from cavity details or dissipation.

What would settle it

Numerical diagonalization of the full emitter-cavity Hamiltonian for a finite quasiperiodic chain that shows mobility edges at locations different from those predicted by the duality mapping, or that shows hopping amplitudes deviating from pure exponential decay or pure sinusoidal oscillation.

Figures

Figures reproduced from arXiv: 2606.10585 by H. T. Cui, H. Z. Shen, M. Qin, X. X. Yi.

Figure 1
Figure 1. Figure 1: (Color online) (a) Schematic for the emitter-cavity [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (Color online) Comparative diagrams of the inverse participation ratio (a1)-(a3) and the fractal dimension (b1)-(b3) [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (Color online) The long-term temporal evolution of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
read the original abstract

The manipulation of localization in quasiperiodic systems by mobility edges or localization transition holds significant physical importance. In this letter, we demonstrated that the dissipation can induce the emergence of anomalous mobility edges and extended-localized transition in emitter-cavity arrays controlled by quasiperiodic potentials. Specifically, we observe that the localization properties of emitters is governed by the nature of quantum bound states, either discrete or embedded in continuum, providing a unified mechanism linking the emitter-photon bound physics to quasiperiodic criticality. Depending on the bound state discrete or continuumlike, the induced effective excitation hopping exhibits either exponentially decaying or sinusoidally oscillating, giving rise to the formation of localized or critical states, respectively. Through a generalized duality transformation, we analytically determine the anomalous mobility edges and the critical strength of potential, enabling the construction of a full phase diagram. The study reveals that the physical characteristics of cavity exert a significant influence on excitation localization. Therefore, the manipulation of excitation localization can be achieved solely by adjusting the cavity fields.

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 / 1 minor

Summary. The paper claims that dissipation in quasiperiodic emitter-cavity arrays induces anomalous mobility edges and extended-localized transitions. Localization properties of emitters are governed by whether quantum bound states are discrete or embedded in the continuum; this determines whether the induced effective excitation hopping is exponentially decaying (yielding localized states) or sinusoidally oscillating (yielding critical states). A generalized duality transformation is used to analytically determine the mobility edges and critical potential strength, constructing a full phase diagram that depends on cavity-field characteristics.

Significance. If the central mapping holds, the work supplies an analytical route to mobility edges in open quasiperiodic systems by linking emitter-photon bound-state physics to criticality. The explicit construction of the phase diagram via duality and the emphasis on cavity control are strengths that could aid quantum simulation of localization transitions.

major comments (2)
  1. [effective hopping derivation (bound-state projection)] The derivation of the effective excitation hopping (section presenting the bound-state projection and resulting hopping form): the manuscript states that discrete bound states produce strictly exponentially decaying hopping while continuum-embedded states produce strictly sinusoidally oscillating hopping, with this form directly mapping to localized versus critical states. No explicit demonstration is given that the quasiperiodic potential acting on the cavity modes or residual dissipation terms do not generate additional corrections; such corrections would invalidate the direct mapping and the subsequent analytic duality.
  2. [duality transformation and phase diagram] Generalized duality transformation and mobility-edge calculation: the analytic determination of the anomalous mobility edges and critical potential strength rests on the effective hopping being exactly of the claimed exponential or sinusoidal form. If the effective model contains unaccounted terms, the duality no longer yields the reported phase boundaries; the manuscript must verify that the transformation remains exact under the full Hamiltonian.
minor comments (1)
  1. [abstract and introduction] The abstract asserts an 'analytical determination' but the main text should include a brief statement of the approximations (if any) used in the bound-state elimination step.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The two major comments both concern the rigor of the effective-model derivation and the exactness of the subsequent duality. We address each point below and indicate where additional material will be supplied.

read point-by-point responses

  1. Referee: [effective hopping derivation (bound-state projection)] The derivation of the effective excitation hopping (section presenting the bound-state projection and resulting hopping form): the manuscript states that discrete bound states produce strictly exponentially decaying hopping while continuum-embedded states produce strictly sinusoidally oscillating hopping, with this form directly mapping to localized versus critical states. No explicit demonstration is given that the quasiperiodic potential acting on the cavity modes or residual dissipation terms do not generate additional corrections; such corrections would invalidate the direct mapping and the subsequent analytic duality.

    Authors: The effective hopping is obtained by projecting the single-excitation dynamics onto the emitter subspace after eliminating the cavity degrees of freedom via the exact bound-state solutions of the local emitter-cavity Hamiltonian. Because the quasiperiodic potential is applied only to the emitters (as stated in the model definition), it does not act directly on the cavity modes that are traced out; any indirect effect appears only through virtual processes that are already resummed into the bound-state wave functions. Residual non-Markovian or multi-excitation corrections are exponentially small in the large-detuning regime used throughout the paper. Nevertheless, we agree that an explicit bound on these corrections was not supplied. In the revised manuscript we will add an appendix that (i) writes the full projected Hamiltonian before truncation and (ii) shows that the neglected terms are O(1/Δ) or higher, where Δ is the cavity-emitter detuning, thereby justifying the claimed exponential or sinusoidal forms. revision: partial

  2. Referee: [duality transformation and phase diagram] Generalized duality transformation and mobility-edge calculation: the analytic determination of the anomalous mobility edges and critical potential strength rests on the effective hopping being exactly of the claimed exponential or sinusoidal form. If the effective model contains unaccounted terms, the duality no longer yields the reported phase boundaries; the manuscript must verify that the transformation remains exact under the full Hamiltonian.

    Authors: The generalized duality is constructed directly on the effective emitter Hamiltonian whose hopping matrix elements are precisely the exponential or sinusoidal functions derived in the preceding section. Because that effective Hamiltonian is obtained by an exact projection (within the single-excitation manifold and the stated detuning regime), the duality transformation remains exact on the effective model. The full microscopic Hamiltonian, however, contains the cavity degrees of freedom that were eliminated; the duality does not act on those degrees of freedom. We will therefore add a short paragraph clarifying the domain of exactness: the analytic mobility edges and phase boundaries are exact for the effective emitter model, and the mapping to the original system is controlled by the same small parameter already bounded in the new appendix. This does not alter the reported phase diagram but makes the range of validity explicit. revision: partial

Circularity Check

0 steps flagged

No circularity; effective model and duality presented as derived from bound-state physics without reduction to inputs

full rationale

The abstract and available description frame the effective hopping (exponentially decaying for discrete bound states, sinusoidally oscillating for continuum-embedded) as a physical consequence of the bound-state nature, which then maps to localized vs. critical states and enables a generalized duality for mobility edges. No quoted equations or self-citations are provided that reduce any central claim (e.g., the duality or phase diagram) to a fitted parameter, self-definition, or prior author result by construction. The derivation chain appears self-contained against external benchmarks of bound-state elimination and quasiperiodic models, with the cavity influence treated as an independent physical input rather than a tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete and based solely on statements in the abstract.

axioms (1)
  • domain assumption Effective excitation hopping is exponentially decaying when bound states are discrete and sinusoidally oscillating when bound states are continuum-embedded.
    This mapping is invoked in the abstract as the direct cause of localized versus critical states.

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    DISSIPATION INDUCED ANOMALOUS MOBILITY EDGES IN A QUASIDISORDERED ATOM-CAVITY CHAIN

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    (S10), i.e

    Case A: E−ω c 2J >1 In this situation, there are two roots for Eq. (S10), i.e. z± = E−ω c 2J ± s E−ω c 2J 2 −1,(S11) which satisfies relationz +z− = 1. For convenience, we introduce the following definition coshx= E−ω c 2J ,sinhx= s E−ω c 2J 2 −1.(S12) It is obvious forE < ω c that|z −|>1 and the singular point is justz +. By residual theorem, one has g2 ...

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    Since the two roots are located on the contour, one can deform the contour aroundz ±, as shown in Fig

    Case B: ωc −E 2J ≤1 The two roots can be written as z± = E−ω c 2J ±i s 1− E−ω c 2J 2 .(S15) Defining cosθ= E−ω c 2J ,sinθ= s 1− E−ω c 2J 2 ,(S16) 3 one can findz ± =e ±iθ. Since the two roots are located on the contour, one can deform the contour aroundz ±, as shown in Fig. S1. Consequently, one has g2 2πi I |z|=1 z|n−n′| −J z2 + (E−ω c)z−J =− g2 2J   z...

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    Case A: ωc −E 2J >1andE > ω c By Eq. (4), one can obtain ∆ cos 2πβn− E ∆ αn + g2 2Jsinhx X n′ e−|n−n′|xαn′ = 0.(S19) In this case, we introduce the generalized duality transformation defined as αk = X n ei2πβnk Tn(x0)αn, Tn(x0)αn = X k e−i2πβnk αk.(S20) T −1 n (x0) = +∞X m=−∞ e−x0|m|ei2πβnm = sinhx 0 cos 2πβn−coshx 0 ,(S21) where coshx 0 = E ∆. Notably, T...

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    Case B: ωc −E 2J >1andE < ω c In this situation, one can find by Eq. (4) ∆ cos 2πβn− E ∆ αn − g2 2Jsinhx X n′ (−1)|n−n′| e−|n−n′|xαn′ = 0.(S29) Adopting the similar approach above, we defineT n (x0) as T −1 n (x0) = +∞X m=−∞ e−x0|m| (−1)|m| ei2πβnm =− sinhx 0 cos 2πβn+ coshx 0 ,(S30) where coshx 0 =− E ∆. Thus, it is found ∆ cos 2πβn− E ∆ αn =−∆ sinhx 0Tn...

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    Case C: ωc −E 2J <1 One obtains by Eq.(4) ∆ cos 2πβn− E ∆ αn − g2 2Jsinθ X n′ sin (|n−n ′|θ)α n′ = 0.(S37) We defineT n (x0) as T −1 n (θ) = N−1X m=−(N−1) sin (|m|θ)e i2πβnm = sinN θcos 2πβn(N−1)−sinθ−sin (N−1)θcos 2πβnN cosθ−cos 2πβnN .(S38) UnderN→ ∞, sin (N−1)θ∼sinN θand cos 2πβn(N−1)∼cos 2πβnN. One thus gets T −1 n (θ)≃ sinθ cos 2πβnN−cosθ .(S39) Defi...

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    Discussion Interestingly, mobility edgeE c for three cases satisfies the same equation in form, i.e. Ec −ω c 2J = Ec ∆ .(S45) However, it should be emphasized thatE c cannot be derived directly by the equation above because the relationship betweenE−ω c and 2Jimposes a fundamental restriction onE c. As shown in the previous derivations, the general dualit...

  53. [53]

    By ωc−Ec 2J = 1, we obtain Ec =ω c ±2J.(S47)

  54. [54]

    By Ec ∆ = 1, we obtain Ec =±∆.(S48)

  55. [55]

    (S45), one getsE c = ∆ωc ∆−2J

    By Eq. (S45), one getsE c = ∆ωc ∆−2J . Substituting the relation into Eq. (S46), we find the critical quasiperiodic potential strength ∆ c ∆c =±ω c + 2J.(S49) 7 1 12 23 34 -2.062 -0.907 0.913 2.868 E/g Δ=1(ωc=0.5) 1 12 23 34 -2.868 -0.870 0.970 2.062 E/g Δ=1(ωc=-0.5) 1 12 23 34 -2.976 -1.902 1.481 2.469 E/g Δ=2(ωc=-0.5) 1 12 23 34 -4.231 -1.494 2.486 n E/...