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arxiv: 2604.10731 · v1 · submitted 2026-04-12 · ❄️ cond-mat.dis-nn · cond-mat.stat-mech

Recognition: unknown

Anderson localization via Peierls phase modulation

Arpita Goswami , Pallabi Chatterjee , Ranjan Modak , Shaon Sahoo
Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:23 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn cond-mat.stat-mech
keywords Anderson localizationPeierls phasetwo-leg ladderquasiperiodic modulationmagnetic fieldAubry-André modellocalization transitionphase diagram
0
0 comments X

The pith

Random Peierls phases localize all eigenstates in a two-leg ladder, while quasiperiodic phases produce a tunable delocalized-to-localized transition.

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

The paper examines a clean two-leg ladder lattice where an external magnetic field is incorporated solely through Peierls phases added to the hopping amplitudes along one leg. A constant uniform phase leaves every eigenstate extended, but random phases, which correspond to a disordered magnetic field, localize all states. Quasiperiodic phase modulations drive a transition between fully delocalized and fully localized regimes, and the authors map the phase diagram for a two-parameter version that mimics a generalized Aubry-André form, revealing delocalized, localized, and mixed regions. A semiclassical analysis yields a qualitatively similar diagram. This establishes a route to controlling localization and transport purely through phase engineering rather than onsite or hopping disorder.

Core claim

In a two-leg ladder described by a clean tight-binding model, uniform Peierls phases keep all eigenstates delocalized, random Peierls phases produce complete Anderson localization of every eigenstate, and quasiperiodic Peierls phase modulations induce a transition from delocalized to localized phases whose diagram for the two-parameter case shows extended, localized, and intermediate mixed regimes.

What carries the argument

Peierls phases inserted into the hopping amplitudes along the ladder legs to encode the magnetic flux in the Landau gauge.

If this is right

  • Random Peierls phases induce complete Anderson localization without introducing disorder in onsite potentials or hopping magnitudes.
  • Quasiperiodic modulation of the Peierls phase drives a transition from a fully delocalized to a fully localized phase as the quasiperiodicity parameter is tuned.
  • The phase diagram for the two-parameter quasiperiodic Peierls phase contains distinct regions of delocalized states, localized states, and intermediate mixed phases.
  • Semiclassical analysis qualitatively reproduces the same localization transition and phase boundaries found in the full quantum treatment.

Where Pith is reading between the lines

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

  • Phase-only modulation separates the control of localization from potential disorder, which may simplify experiments in artificial gauge-field platforms.
  • The mixed-phase regions could contain states with intermediate localization lengths or multifractal properties that affect transport in distinct ways.
  • Analogous phase-engineering mechanisms might produce localization transitions in other quasi-one-dimensional or ladder geometries.

Load-bearing premise

The magnetic field affects the ladder only by adding phases to the hopping terms via the Peierls substitution, with the tight-binding model remaining valid and no extra orbital or interaction effects present.

What would settle it

Numerical diagonalization or an experiment that finds extended eigenstates persisting under fully random Peierls phases, or that shows no localization transition as the quasiperiodicity strength is increased, would falsify the central claims.

Figures

Figures reproduced from arXiv: 2604.10731 by Arpita Goswami, Pallabi Chatterjee, Ranjan Modak, Shaon Sahoo.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematic diagram of the model system, [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Schematic phase diagram corresponding to the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Uniform magnetic flux: Average IPR vs. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Uniform magnetic flux [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Random magnetic flux: Average PR vs. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Random magnetic flux [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Quasiperiodic magnetic flux ( [PITH_FULL_IMAGE:figures/full_fig_p007_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: A more detailed study of the Lyapunov exponent can be found in Appendix B. These results are in com￾plete agreement with the behavior observed in our study of ⟨P R⟩. Now, from the previous analyses based on the [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 2
Figure 2. Figure 2: In this section, we present the numerical results [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Quasiperiodic magnetic flux ( [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Quasiperiodic magnetic flux ( [PITH_FULL_IMAGE:figures/full_fig_p008_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Quasiperiodic magnetic flux ( [PITH_FULL_IMAGE:figures/full_fig_p009_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Quasiperiodic magnetic flux ( [PITH_FULL_IMAGE:figures/full_fig_p009_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: Quasiperiodic magnetic flux ( [PITH_FULL_IMAGE:figures/full_fig_p010_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: Classical trajectory evolution for magnetic flux [PITH_FULL_IMAGE:figures/full_fig_p011_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17: Finite size extrapolation of (a) [PITH_FULL_IMAGE:figures/full_fig_p016_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18: Quasiperiodic magnetic flux ( [PITH_FULL_IMAGE:figures/full_fig_p017_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19: Quasiperiodic magnetic flux ( [PITH_FULL_IMAGE:figures/full_fig_p017_19.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21: Quasiperiodic magnetic flux ( [PITH_FULL_IMAGE:figures/full_fig_p018_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22: Quasiperiodic magnetic flux ( [PITH_FULL_IMAGE:figures/full_fig_p018_22.png] view at source ↗
read the original abstract

We investigate a two leg ladder system subjected to an external magnetic field. In the absence of a magnetic field, the system is described by a clean tight binding model, with no disorder in either the onsite potential or the hopping amplitudes. The effect of magnetic field in this system is studied by introducing the Peierls phases in the hopping amplitudes along a leg (appropriate when the Landau gauge is chosen). For a uniform magnetic field, characterized by a constant Peierls phase, we find that all eigenstates remain delocalized. In contrast, random Peierls phases, representing a random magnetic field, lead to complete localization of the eigenstates. We further show that a quasiperiodic modulation of the Peierls phase can drive a transition from a fully delocalized to a fully localized phase upon tuning the quasiperiodicity. For a two parameter quasiperiodic Peierls phase, varying analogously to a generalized Aubry Andre type potential, we construct the phase diagram of the system. The phase diagram exhibits regions of delocalized and localized phases, separated by intermediate regimes of mixed phase. We also perform a semiclassical analysis that qualitatively yields a similar phase diagram, capturing the localization transition. Our results demonstrate a mechanism for controlling transport properties via the Peierls phase engineering.

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

0 major / 4 minor

Summary. The manuscript examines Anderson localization in a two-leg tight-binding ladder by introducing Peierls phases into the hopping terms along one leg. Uniform (constant) phases leave all eigenstates delocalized, while random phases produce complete localization. Quasiperiodic modulation of the phases, constructed analogously to a generalized Aubry-André potential, drives a delocalized-to-localized transition; the resulting two-parameter phase diagram contains delocalized, localized, and intermediate mixed-phase regions. A semiclassical analysis is shown to reproduce the qualitative features of the numerically obtained diagram.

Significance. If the central claims hold, the work demonstrates a route to localization that relies solely on phase modulation of hoppings rather than onsite disorder, which is directly relevant to synthetic gauge-field experiments in cold atoms and superconducting circuits. The direct mapping of the quasiperiodic phase problem onto an Aubry-André-like model, together with the supporting semiclassical treatment, provides a clean and falsifiable extension of known localization physics to ladder geometries.

minor comments (4)
  1. The numerical section should state the system sizes, boundary conditions, and convergence criteria used for the inverse participation ratio (IPR) calculations that underlie the phase diagram; without these details the sharpness of the reported transitions cannot be assessed.
  2. The precise operational definition of the 'mixed phase' (e.g., any IPR threshold, fraction of states, or finite-size scaling criterion) is not given; this quantity appears in the abstract and phase-diagram discussion and should be defined explicitly.
  3. The semiclassical analysis is described as qualitative; a brief outline of the key approximations (e.g., which terms are retained in the effective potential) would help readers judge the regime of validity.
  4. Figure captions should indicate the precise parameter values and system sizes corresponding to each panel so that the data can be reproduced from the text alone.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and accurate summary of our manuscript, the recognition of its significance for synthetic gauge-field experiments, and the recommendation of minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's derivation proceeds from the standard two-leg ladder tight-binding Hamiltonian with Peierls phases inserted on one leg. Random phases produce effective disorder because rung couplings prevent global gauging, directly yielding Anderson localization via standard numerics (IPR, participation ratio). Quasiperiodic modulation is constructed analogously to the Aubry-André potential but applied to the phase channel, with the phase diagram obtained from direct diagonalization. The semiclassical analysis is presented as a qualitative independent check that reproduces the same transition boundaries without fitting parameters to the numerical data. No equation reduces a claimed prediction to an input by construction, no load-bearing self-citation justifies a uniqueness theorem or ansatz, and the model assumptions (Peierls substitution validity) are stated explicitly without circular redefinition. The results are self-contained against external benchmarks of Anderson localization and quasiperiodic models.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The claims rest on the standard tight-binding description of a ladder and the validity of the Peierls substitution for magnetic fields; no new free parameters or entities are introduced in the abstract.

axioms (2)
  • domain assumption The ladder is described by a non-interacting tight-binding Hamiltonian with Peierls phases in the hoppings.
    Standard modeling choice for electrons in a lattice under magnetic field.
  • domain assumption Localization is diagnosed from eigenstate properties such as inverse participation ratio.
    Common numerical proxy in Anderson localization studies.

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Reference graph

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