Delocalization and re-entrant localization of flat-band states in non-Hermitian disordered lattice models with flat bands

Kim, Sang-Bum; Kim, Kihong

doi:10.1093/ptep/ptac162

Cited by 2 publications

(1 citation statement)

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“…Despite extensive studies on Anderson localization [3][4][5][6][7][8], there are still several aspects that are not fully understood, and new types of localization phenomena continue to be discovered . Recent examples include unconventional transport in disordered quantum wires [9][10][11][12][13], localization in disordered non-Hermitian systems [14][15][16][17][18][19][20], and the quantum boomerang effect in both Hermitian and non-Hermitian systems [21][22][23][24][25]. Furthermore, the effect of interactions on Anderson localization and the related phenomenon of many-body localization has been an important and challenging research topic for many decades that still raises many open questions [34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Transport and localization properties of excitations in one-dimensional lattices with diagonal disordered mosaic modulations

Nguyen,

Kim

2023

J. Phys. A: Math. Theor.

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We present a numerical study of the transport and localization properties of excitations in one-dimensional lattices with diagonal disordered mosaic modulations. The model is characterized by the modulation period $\kappa$ and the disorder strength $W$. We calculate the disorder averages $\langle T\rangle$, $\langle \ln T\rangle$, and $\langle P\rangle$, where $T$ is the transmittance and $P$ is the participation ratio, as a function ofenergy $E$ and system size $L$, for different values of $\kappa$ and $W$. For excitations at quasiresonance energies determined by $\kappa$, we find power-law scaling behaviors of the form $\langle T \rangle \propto L^{-\gamma_{a}}$,$\langle \ln T \rangle \approx -\gamma_g \ln L$, and $\langle P \rangle \propto L^{\beta}$, as $L$ increases to a large value.In the strong disorder limit, the exponents are seen to saturate at the values $\gamma_a \sim 0.5$, $\gamma_g \sim 1$, and $\beta\sim 0.3$,regardless of the quasiresonance energy value. This behavior is in contrast to the exponentiallocalization behavior occurring at all other energies.The appearance of sharp peaks in the participation ratio spectrum at quasiresonance energies provides additional evidence for the existence of an anomalous power-law localization phenomenon.The corresponding eigenstates demonstrate multifractal behavior and exhibit unique node structures.In addition, we investigate the time-dependent wave packet dynamics and calculate the mean square displacement $\langle m^2(t) \rangle$, spatial probability distribution, participation number, and return probability.When the wave packet's initial momentum satisfies the quasiresonance condition, weobserve a subdiffusive spreading of the wave packet, characterized by $\langle m^2(t) \rangle\propto t^{\eta}$ where $\eta$ is always less than 1.We also note the occurrence of partial localization at quasiresonance energies, as indicated by the saturation of the participation number and a nonzero value for the return probability at long times.

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