Hidden dualities in 1D quasiperiodic lattice models

Gonçalves, Miguel; Amorim, B.; Castro, Eduardo V.; Ribeiro, Pedro

doi:10.21468/scipostphys.13.3.046

Cited by 24 publications

(2 citation statements)

References 56 publications

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“…Unlike several recent works [46][47][48][49][50], here for the emergence of the mobility edge, robust at the large potential, we need neither the special flat-band structure of the disorder-free model [46][47][48]51] nor correlated disorder [49,50,[52][53][54][55][56]. Our model is based on the i.i.d.…”

Section: Introductionmentioning

confidence: 99%

Robust extended states in Anderson model on partially disordered random regular graphs

Kochergin,

Khaymovich,

Valba

et al. 2024

SciPost Phys.

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In this work we analytically explain the origin of the mobility edge in the partially disordered random regular graphs of degree d, i.e., with a fraction \betaβ of the sites being disordered, while the rest remain clean. It is shown that the mobility edge in the spectrum survives in a certain range of parameters (d,\betaβ) at infinitely large uniformly distributed disorder. The critical curve separating extended and localized states is derived analytically and confirmed numerically. The duality in the localization properties between the sparse and extremely dense RRG has been found and understood.

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Section: Introductionmentioning

confidence: 99%

Robust extended states in Anderson model on partially disordered random regular graphs

Kochergin,

Khaymovich,

Valba

et al. 2024

SciPost Phys.

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“…In Ref. [12] the authors developed a renormalization-group theory to describe the localization properties of quasiperiodic systems. That theory can be used to obtain exact or approximate analytical expressions for the phase boundaries of extended, localized and critical phases for specific models.…”

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confidence: 99%

Predicted Critical State Based on Invariance of the Lyapunov Exponent in Dual Spaces

Liu 刘,

Xia 夏

2024

Chinese Phys. Lett.

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The critical state in disordered systems, a fascinating and subtle eigenstate, has attracted a lot of research interest. However, the nature of the critical state is difficult to describe quantitatively, and in general, it cannot predict a system that hosts the critical state. In this work, we propose an explicit criterion that the Lyapunov exponent of the critical state should be 0 simultaneously in dual spaces, namely Lyapunov exponent remains invariant under the Fourier transform. With this criterion, we exactly predict a one-dimensional quasiperiodic model which is not self-duality, but hosts a large number of critical states. Then, we perform numerical verification of the theoretical prediction and display the self-similarity of the critical state. Due to computational complexity, higher dimensional models are not performed calculations, however, since the description of extended and localized states by the Lyapunov exponent is universal and dimensionless, utilizing the Lyapunov exponent of dual spaces to describe critical states should also be universal. Finally, we conjecture that there exists some kind of connection between the invariance of the Lyapunov exponent and conformal invariance, which can promote the research of critical phenomena.

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Observation of reentrant metal-insulator transition in a random-dimer disordered SSH lattice

Xu,

Gao,

Iovan

et al. 2024

npj Nanophoton.

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The interrelationship between localization, quantum transport, and disorder has remained a fascinating focus in scientific research. Traditionally, it has been widely accepted in the physics community that in one-dimensional systems, as disorder increases, localization intensifies, triggering a metal-insulator transition. However, a recent theoretical investigation [Phys. Rev. Lett. 126, 106803] has revealed that the interplay between dimerization and disorder leads to a reentrant localization transition, constituting a remarkable theoretical advancement in the field. Here, we present the first experimental observation of reentrant localization using an experimentally friendly model, a photonic SSH lattice with random-dimer disorder, achieved by incrementally adjusting synthetic potentials. In the presence of correlated on-site potentials, certain eigenstates exhibit extended behavior following the localization transition as the disorder continues to increase. We directly probe the wave function in disordered lattices by exciting specific lattice sites and recording the light distribution. This reentrant phenomenon is further verified by observing an anomalous peak in the normalized participation ratio. Our study enriches the understanding of transport in disordered mediums and accentuates the substantial potential of integrated photonics for the simulation of intricate condensed matter physics phenomena.

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Hidden dualities in 1D quasiperiodic lattice models

Cited by 24 publications

References 56 publications

Robust extended states in Anderson model on partially disordered random regular graphs

Robust extended states in Anderson model on partially disordered random regular graphs

Predicted Critical State Based on Invariance of the Lyapunov Exponent in Dual Spaces

Observation of reentrant metal-insulator transition in a random-dimer disordered SSH lattice

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