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Related papers: Exact mobility edges in Aubry-Andr\'{e}-Harper mod…

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We study a non-Hermitian Aubry-Andr\'e-Harper model with both nonreciprocal hoppings and complex quasiperiodical potentials, which is a typical non-Hermitian quasicrystal. We introduce boundary-dependent self-dualities in this model and…

Disordered Systems and Neural Networks · Physics 2021-01-20 Xiaoming Cai

We study localization in a one-dimensional quasiperiodic lattice obtained by extending the Aubry-Andr\'e model with an additional $N$th-neighbor hopping term of strength $J_{N}$. This long-range tunneling couples successive windings of an…

Disordered Systems and Neural Networks · Physics 2026-05-19 Taylan Yildiz , B. Tanatar , Balázs Hetényi

We study one-dimensional lattices with imaginary-valued Aubry-Andre-Harper (AAH) potentials. Such lattices can host edge states with purely imaginary eigenenergies, which differ from the edge states of the Hermitian AAH model and are…

Quantum Physics · Physics 2024-10-25 Bofeng Zhu , Li-Jun Lang , Qiang Wang , Qi Jie Wang , Y. D. Chong

We investigate localization properties in a family of deterministic (i.e. no disorder) nearest neighbor tight binding models with quasiperiodic onsite modulation. We prove that this family is self-dual under a generalized duality…

Disordered Systems and Neural Networks · Physics 2015-04-16 Sriram Ganeshan , J. H. Pixley , S. Das Sarma

We explore properties of a Gross-Pitaevskii chain subject to an incommensurate periodic potential, i.e., a nonlinear Aubry-Andre model. We show that the condensate crucially impacts the properties of the elementary excitations. In contrast…

Disordered Systems and Neural Networks · Physics 2025-11-25 Oleg I. Utesov , Yeongjun Kim , Sergej Flach

We demonstrate the existence of an intermediate super-exponential localization regime for eigenstates of the Aubry-Andr\'e chain. In this regime, the eigenstates localize factorially similarly to the eigenstates of the Wannier-Stark ladder.…

Quantum Gases · Physics 2023-08-16 Arindam Mallick , Alexei Andreanov , Sergej Flach

Consider a random block matrix model consisting of $D$ random systems arranged along a circle, where each system is modeled by an independent $N\times N$ complex Hermitian Wigner matrix. Neighboring systems interact via an arbitrary…

Probability · Mathematics 2025-07-14 Jiaqi Fan , Bertrand Stone , Fan Yang , Jun Yin

Sil, Maiti, and Chakrabarti (SMC) (Phys. Rev. Lett. 101, 076803 (2008), arXiv:0801.2670) introduce an aperiodic two-leg ladder network composed of atomic sites with on-site potentials distributed according to a quasiperiodic Aubry-Andre…

Disordered Systems and Neural Networks · Physics 2014-02-13 Sergej Flach , Carlo Danieli

In one-dimensional Hermitian tight-binding models, mobility edges separating extended and localized states can appear in the presence of properly engineered quasi-periodical potentials and coupling constants. On the other hand, mobility…

Disordered Systems and Neural Networks · Physics 2022-07-27 Cem Yuce , Hamidreza Ramezani

We introduce a conceptual reformulation of the Mott-Berezinski\u{i} (MB) theory of low-frequency AC conductivity in disordered systems based on localization landscape theory. Instead of assuming uniform localization and fixed hopping…

Disordered Systems and Neural Networks · Physics 2025-12-30 Gabriel Hayoun , Ilya A. Gruzberg , Marcel Filoche

By analyzing the Lyapunov exponent (LE), we develop a rigorous, fundamental scheme for the study of general non-Hermitian quasicrystals with both complex phase factor and non-reciprocal hopping. Specially, the localization-delocalization…

Disordered Systems and Neural Networks · Physics 2021-07-07 Yanxia Liu , Qi Zhou , Shu Chen

An exact analytical diagonalization is used to solve the two dimensional Extended Hubbard Model for system with finite size. We have considered an Extended Hubbard Model (EHM) including on-site and off-site interactions with interaction…

Statistical Mechanics · Physics 2015-06-03 S. Harir , M. Bennai , Y. Boughaleb

In this paper, a non-Hermitian Aubry-Andr\'e-Harper model with power-law hoppings ($1/s^{a}$) and quasiperiodic parameter $\beta$ is studied, where $a$ is the power-law index, $s$ is the hopping distance, and $\beta$ is a member of the…

Disordered Systems and Neural Networks · Physics 2023-05-24 Dechi Peng , Shujie Cheng , Gao Xianlong

We analyse the eigenvectors of the adjacency matrix of the Erd\H{o}s-R\'enyi graph $\mathbb G(N,d/N)$ for $\sqrt{\log N} \ll d \lesssim \log N$. We show the existence of a localized phase, where each eigenvector is exponentially localized…

Probability · Mathematics 2023-12-21 Johannes Alt , Raphael Ducatez , Antti Knowles

Non-Hermitian extensions of the Aubry-Andr\'e-Harper (AAH) model reveal a rich variety of phase transitions arising from the interplay of quasiperiodicity and non-Hermiticity. Despite their theoretical significance, experimental…

Quantum Physics · Physics 2025-08-12 Quan Lin , Christopher Cedzich , Qi Zhou , Peng Xue

We identify steerable exponentially localized in-gap mode in a quasiperiodic non-Hermitian Aubry-Andr\'e-Harper chain with a spatially fluctuating, zero-mean imaginary gauge field. Under open boundary conditions, the system is exactly…

Optics · Physics 2026-01-21 Yazhuang Miao , Wei Ding , Litong Wang , Xiaolong Zhao , Shengguang Liu , Xuexi Yi

We introduce and study a new class of Banded Random Matrix model describing sparse, long range quantum hopping in one dimension. Using a series of analytic arguments, numerical simulations, and mappings to statistical physics models, we…

Statistical Mechanics · Physics 2017-06-16 Xiangyu Cao , Alberto Rosso , Jean-Philippe Bouchaud , Pierre Le Doussal

A new supersymmetric model for electrons with generalized hopping terms and Hubbard interaction on a one-dimensional lattice is solved by means of the Bethe Ansatz. We investigate the phase diagram of this model by studying the ground state…

Condensed Matter · Physics 2009-10-28 Gerald Bedürftig , Holger Frahm

We study Anderson localization in a discrete-time quantum map dynamics in one dimension with nearest-neighbor hopping strength $\theta$ and quasienergies located on the unit circle. We demonstrate that strong disorder in a local phase field…

Disordered Systems and Neural Networks · Physics 2023-06-28 Ihor Vakulchyk , Sergej Flach

We propose an one-dimensional generalized Aubry-Andr{\'e}-Harper (AAH) model with off-diagonal hopping and staggered on-site potential. We find that the localization transitions could be multiple reentrant with the increasing of staggered…

Disordered Systems and Neural Networks · Physics 2023-06-05 Rui Qi , Junpeng Cao , Xiang-Ping Jiang