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Engineering Anderson Localization in Arbitrary Dimensions with Interacting Quasiperiodic Kicked Bosons

T0 review · 2 major / 2 minor · reviewed 2026-05-18 · grok-4.3

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Pith's one-line read Both interparticle interactions and quasiperiodic modulations generate synthetic dimensions for Anderson localization.

desk verdict Interactions plus quasiperiodic kicks in a 1D boson gas generate effective 2D-4D Anderson models via synthetic dimensions, with numerics showing localization but the mapping extension left partly implicit. read the letter →

arxiv 2511.05344 v2 submitted 2025-11-07 cond-mat.quant-gas cond-mat.dis-nn

H. Olsen , P. Vignolo , M. Albert This is my paper · ORCID
classification cond-mat.quant-gascond-mat.dis-nn
keywords AndersonlocalizationsyntheticdimensionsquasiperiodicdrivingkickedrotorLieb-Linigerbosonstwo-bodydynamicstransitionorthogonaluniversalityclass
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper explores the Lieb-Liniger model of one-dimensional bosons under periodic delta kicks, incorporating interparticle interactions and quasiperiodic variations in kicking strength. It shows that these interactions alone can create an effective two-dimensional Anderson model through the known kicked rotor mapping. Adding one or two incommensurate frequencies extends the effective dimensionality to three or four. Numerical studies of two-body dynamics with finite-time scaling confirm Anderson localization and the orthogonal critical behavior. The method thus allows emulation of localization phenomena in higher dimensions using one-dimensional systems.

What carries the argument

The extended mapping of the interacting kicked rotor to a higher-dimensional Anderson model, where interactions and quasiperiodic frequencies serve as generators of synthetic dimensions.

What would settle it

A failure of the finite-time scaling to show the expected orthogonal universality class critical exponents in the two-body participation ratio for the three- or four-dimensional cases would falsify the claim.

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Extended reading notes

Core claim

Both interparticle interactions and quasiperiodic modulations of the kicking strength can independently and simultaneously generate synthetic dimensions. In the absence of modulation, interactions between two bosons already promote an effective two-dimensional Anderson model. Introducing one or two additional incommensurate frequencies further extends the system to three and four effective dimensions. Through extensive numerical simulations of the two-body dynamics and finite-time scaling analysis, Anderson localization and the associated critical behavior characteristic of the orthogonal universality class are observed.

Load-bearing premise

The standard mapping from the kicked rotor to the Anderson model still applies when interactions and quasiperiodic modulations are added to the system.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The paper studies the Lieb-Liniger Hamiltonian for two bosons in one dimension subjected to periodic delta kicks, with optional quasiperiodic modulation of the kick strength. Building on the single-particle kicked-rotor–Anderson mapping, it argues that interparticle interactions alone generate an effective two-dimensional Anderson model via center-of-mass and relative coordinates, while one or two additional incommensurate frequencies extend the synthetic dimension count to three or four. Extensive two-body numerical simulations combined with finite-time scaling are used to report Anderson localization and critical exponents consistent with the orthogonal universality class.

Significance. If the mapping and numerical evidence hold, the work supplies a controllable route to Anderson localization and its mobility-edge physics in synthetic dimensions d=2,3,4 using only one-dimensional interacting bosons, which is of clear interest for quantum-gas experiments. The explicit use of finite-time scaling to extract universality-class signatures is a methodological strength.

major comments (2)
  1. [§2–3] §2–3 (model and mapping): The central claim that the Floquet operator of the interacting, modulated kicked Lieb-Liniger system maps onto a non-interacting Anderson tight-binding model in synthetic dimensions is stated as an extension of the known single-particle result, but no explicit operator identity, perturbative expansion, or gauge transformation is supplied showing that the interaction term V(|x1−x2|) remains strictly diagonal (on-site) in the center-of-mass/relative lattice basis without generating correlated off-diagonal or long-range hopping. Such terms would alter both the orthogonal-class universality and the location of any mobility edge; their absence must be demonstrated for the load-bearing mapping to be accepted.
  2. [§4] §4 (numerics and scaling): The finite-time scaling analysis reports orthogonal-class critical behavior, yet the manuscript does not quantify how the extracted exponents or the apparent mobility edge shift when the interaction strength or modulation amplitudes are varied over a range that would expose possible residual correlated disorder. A systematic check that the scaling collapse remains stable under these variations is required to confirm that the observed criticality is not an artifact of the two-body truncation or finite-time window.
minor comments (2)
  1. [Figure 3] Figure 3 and associated text: the scaling collapse plots would benefit from explicit error bands on the data points and a statement of the fitting window used for the correlation length.
  2. [§3] Notation: the definition of the synthetic lattice spacing and the precise identification of the on-site disorder strength in the effective Anderson Hamiltonian should be written explicitly rather than left implicit from the single-particle analogy.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and indicate where revisions will be made to strengthen the presentation.

read point-by-point responses

  1. Referee: [§2–3] §2–3 (model and mapping): The central claim that the Floquet operator of the interacting, modulated kicked Lieb-Liniger system maps onto a non-interacting Anderson tight-binding model in synthetic dimensions is stated as an extension of the known single-particle result, but no explicit operator identity, perturbative expansion, or gauge transformation is supplied showing that the interaction term V(|x1−x2|) remains strictly diagonal (on-site) in the center-of-mass/relative lattice basis without generating correlated off-diagonal or long-range hopping. Such terms would alter both the orthogonal-class universality and the location of any mobility edge; their absence must be demonstrated for the load-bearing mapping to be accepted.

    Authors: We agree that an explicit demonstration is required to fully substantiate the mapping. The manuscript presents the result as a direct extension of the single-particle kicked-rotor–Anderson correspondence, with the interaction entering through the relative coordinate. In the revised version we will insert a new subsection deriving the effective Floquet operator in the center-of-mass/relative quasi-momentum basis and explicitly showing that V(|x1−x2|) contributes only a diagonal on-site potential; no correlated off-diagonal or long-range terms appear because the basis states are simultaneous eigenstates of the relative-position operator in the relevant Floquet frame. This addition will confirm that the effective model remains strictly non-interacting Anderson in the orthogonal class. revision: yes

  2. Referee: [§4] §4 (numerics and scaling): The finite-time scaling analysis reports orthogonal-class critical behavior, yet the manuscript does not quantify how the extracted exponents or the apparent mobility edge shift when the interaction strength or modulation amplitudes are varied over a range that would expose possible residual correlated disorder. A systematic check that the scaling collapse remains stable under these variations is required to confirm that the observed criticality is not an artifact of the two-body truncation or finite-time window.

    Authors: For two particles the numerics solve the exact two-body time-dependent Schrödinger equation, so there is no truncation. Nevertheless, we accept that a systematic parameter scan strengthens the claim. In the revised manuscript we will add an appendix (or extended figure) presenting finite-time scaling collapses for several values of the interaction strength and modulation amplitudes. The extracted exponents and mobility-edge location remain consistent with the orthogonal class across this range, indicating that any residual correlated hopping, if present, is negligible within the regime studied. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; claims rest on external mapping plus independent numerics

full rationale

The paper explicitly builds on the established single-particle kicked-rotor–Anderson mapping (cited as known) and then performs extensive numerical simulations of the two-body Floquet dynamics together with finite-time scaling to observe localization and orthogonal-class critical behavior. No equations or steps in the provided text reduce a reported prediction or synthetic-dimension claim to a fitted parameter or self-citation by construction. The central results are supported by direct dynamical evidence rather than by re-labeling inputs, making the derivation self-contained against external benchmarks.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

The claim rests on the validity of extending the kicked-rotor-to-Anderson mapping to the interacting Lieb-Liniger case and on the assumption that two-body numerics plus finite-time scaling suffice to diagnose higher-dimensional localization transitions.

assumptions (1)
  • domain assumption The mapping between the kicked rotor and the Anderson model remains valid when interparticle interactions and quasiperiodic modulations of kick strength are introduced.
    The entire synthetic-dimension construction is built on this extension of the known single-particle mapping.

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Cite this review

Pith. "Pith review of Engineering Anderson Localization in Arbitrary Dimensions with Interacting Quasiperiodic Kicked Bosons." pith.science (2026). https://pith.science/paper/2511.05344

@misc{pith2026251105344,
  author       = {Pith},
  title        = {Pith review of: Engineering Anderson Localization in Arbitrary Dimensions with Interacting Quasiperiodic Kicked Bosons},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2511.05344}},
  note         = {Machine review of arXiv:2511.05344}
}
read the original abstract

We study the interplay of interactions and quasiperiodic driving in the Lieb-Liniger model of one-dimensional bosons subjected to a sequence of delta kicks. Building on the known mapping between the kicked rotor and the Anderson model, we show that both interparticle interactions and quasiperiodic modulations of the kicking strength can independently and simultaneously generate synthetic dimensions. In the absence of modulation, interactions between two bosons already promote an effective two-dimensional Anderson model. Introducing one or two additional incommensurate frequencies further extends the system to three and four effective dimensions, respectively. Through extensive numerical simulations of the two-body dynamics and finite-time scaling analysis, we observe Anderson localization and the associated critical behavior characteristic of the orthogonal universality class. This combined use of interactions and quasiperiodic driving thus provides a versatile framework for emulating Anderson localization and its transition in arbitrary dimensions.

Figures

Figures reproduced from arXiv: 2511.05344 by the authors.

Figure 1
Figure 1. Time evolution of the total energy of the two particles for different values of the [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. The rescaled quantity ln Λ = ln ⟨E(t)⟩/t2/d as a function of K for different times between t = 10 and t = 200. All curves intersect approximately at the critical point demonstrating the existence of a metal-insulator transition and allowing to locate the critical point Kc. Here c = 10, ε = 0.3 and Nω = 1 for the left figure (d = 3) and Nω = 2 for the right one (d = 4). quantity Λ(K, t) = ⟨E(t)⟩t −2/d = f  ξ(K)t −1/… view at source ↗
Figure 3
Figure 3. Finite time scaling applied to the numerical results with [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Determination of the critical exponents ν and s by fitting (ln Λ)′ (Kc, t) as function of t in log-log scale. Here c = 10, ε = 0.3 and Nω = 1, 2 for a) and b). 3 4 5 6 7 0.1 0.2 0.3 0.4 0.5 0.5 0.4 0.3 0.2 0.1 0.0 0.1 K ε Localized a) Delocalized 3 4 5 6 7 0.1 0.2 0.3 …
Figure 5
Figure 5. Figure 5: Phase diagram of the dynamical phases in the [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

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Cited by 1 Pith paper

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Pith tools

Reviewed May 18, 2026 · model on record in the stance chip above.