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Related papers: Exact mobility edges for 1D quasiperiodic models

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We introduce a one-dimensional quasiperiodic mosaic model with analytically solvable mobility edges that exhibit different phase transitions depending on the system parameters. Specifically, by combining mosaic quasiperiodic…

Disordered Systems and Neural Networks · Physics 2025-03-07 Xu Xia , Weihao Huang , Ke Huang , Xiaolong Deng , Xiao Li

In one-dimensional quasiperiodic systems, only a few models with exact mobility edges (MEs) have been constructed using generalized self-duality theory, Avila's global theory, or the renormalization group method. This raises an intriguing…

Disordered Systems and Neural Networks · Physics 2025-12-29 Hai-Tao Hu , Xiaoshui Lin , Ai-Min Guo , Guangcan Guo , Zijin Lin , Ming Gong

A single-particle mobility edge (SPME) marks a critical energy separating extended from localized states in a quantum system. In one-dimensional systems with uncorrelated disorder, a SPME cannot exist, since all single-particle states…

The mobility edge (ME) that marks the energy separating extended and localized states is a central concept in understanding the metal-insulator transition induced by disordered or quasiperiodic potentials. MEs have been extensively studied…

Disordered Systems and Neural Networks · Physics 2023-04-25 Yucheng Wang , Long Zhang , Yuhao Wan , Yu He , Yongjian Wang

We provide approximate solutions for the mobility edge (ME) that demarcates localized and extended states within a specific class of one-dimensional non-Hermitian (NH) quasicrystals. These NH quasicrystals exhibit a combination of…

Disordered Systems and Neural Networks · Physics 2025-02-14 Xiang-Ping Jiang , Mingdi Xu , Lei Pan

We investigate the symmetries of so-called generalized extended CMV matrices. It is well-documented that problems involving reflection symmetries of standard extended CMV matrices can be subtle. We show how to deal with this in an elegant…

Spectral Theory · Mathematics 2024-10-08 Christopher Cedzich , Jake Fillman , Long Li , Darren Ong , Qi Zhou

In this paper, we study a one-dimensional tight-binding model with tunable incommensurate potentials. Through the analysis of the inverse participation rate, we uncover that the wave functions corresponding to the energies of the system…

Disordered Systems and Neural Networks · Physics 2022-02-02 Tong Liu , Yufei Zhu , Shujie Cheng , Feng Li , Hao Guo , Yong Pu

The mobility edges (MEs) that separate localized, multifractal and ergodic states in energy are a central concept in understanding Anderson localization. In this work we study the effect of several mutually commensurate quasiperiodic…

Strongly Correlated Electrons · Physics 2026-04-06 Manish Kumar , Ivan M. Khaymovich , Auditya Sharma

Quasiperiodic systems offer an appealing intermediate between long-range ordered and genuine disordered systems, with unusual critical properties. One-dimensional models that break the so-called self-dual symmetry usually display a mobility…

Quantum Gases · Physics 2022-04-26 Hepeng Yao , Alice Khoudli , Léa Bresque , Laurent Sanchez-Palencia

Conventionally the mobility edge (ME) separating extended states from localized ones is a central concept in understanding Anderson localization transition. The critical state, being delocalized and non-ergodic, is a third type of…

Disordered Systems and Neural Networks · Physics 2022-11-17 Yucheng Wang

We propose quasiperiodic chains with tunable mobility edge physics, as a promising platform for engineering long-range quantum entanglement. Using the generalized Aubry-Andr\'e model, we show that the mobility edges play a key role in…

Strongly Correlated Electrons · Physics 2025-07-10 YouYoung Joung , Junmo Jeon , SungBin Lee

We investigate the appearance of mobility edges in a one-dimensional non-Hermitian tight-banding model with alternating hopping constants and slowly varying quasi-periodic on-site potentials. Due to the presence of slowly varying exponent,…

Disordered Systems and Neural Networks · Physics 2024-11-22 Qiyun Tang , Yan He

We study a one-dimensional quasiperiodic system described by the Aubry-Andr\'e model in the small wave vector limit and demonstrate the existence of almost mobility edges and critical regions in the system. It is well known that the…

Disordered Systems and Neural Networks · Physics 2018-01-03 Yucheng Wang , Gao Xianlong , Shu Chen

The mobility edge, as a central concept in disordered models for localization-delocalization transitions, has rarely been discussed in the context of random matrix theory (RMT). Here we report a new class of random matrix model by direct…

Disordered Systems and Neural Networks · Physics 2023-11-16 Xiaoshui Lin , Guang-Can Guo , Ming Gong

We propose a minimal two-leg ladder model in which the mobility edge (ME) arises solely due to bond modulation, introduced through a slowly varying quasiperiodic modulation in the inter-leg tunnelling amplitudes. We demonstrate that this…

Statistical Mechanics · Physics 2025-12-09 Arpita Goswami

We propose a family of one-dimensional mosaic models inlaid with a slowly varying potential $V_n=\lambda\cos(\pi\alpha n^\nu)$, where $n$ is the lattice site index and $0<\nu<1$. Combinating the asymptotic heuristic argument with the theory…

Disordered Systems and Neural Networks · Physics 2020-12-14 Longyan Gong

We propose a general analytic method to study the localization transition in one-dimensional quasicrystals with parity-time ($\mathcal{PT}$) symmetry, described by complex quasiperiodic mosaic lattice models. By applying Avila's global…

Disordered Systems and Neural Networks · Physics 2021-02-03 Yanxia Liu , Yucheng Wang , Xiong-Jun Liu , Qi Zhou , Shu Chen

In this study, we investigate the problem of Anderson localization in a one-dimensional flat band lattice with a non-Hermitian quasiperiodic on-site potential. First of all, we discuss the influences of non-Hermitian potentials on the…

Disordered Systems and Neural Networks · Physics 2025-06-12 Guang-Xin Pang , Zhi Li , Shan-Zhong Li , Yan-Yang Zhang , Jun-Feng Liu , Yi-Cai Zhang

Mobility edges commonly arise in one-dimensional quasiperiodic systems once exact self-duality is broken, yet their origin is typically understood only at the level of individual Hamiltonians. Here we show that mobility edge positions are…

Disordered Systems and Neural Networks · Physics 2026-05-19 Sanghoon Lee , Tilen Cadez , Kyoung-Min Kim

Mobility edge, a critical energy separating localized and extended excitations, is a key concept for understanding quantum localization. Aubry-Andr\'{e} (AA) model, a paradigm for exploring quantum localization, does not naturally allow…