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Semi-localized ground state in a 1D system with long-range hopping

Year: 2026

Type: preprint

Abstract: We study the localization of a quantum particle in a one-dimensional disordered system with long-range hopping amplitudes $t(r)\propto r^{-a}$. In contrast to the standard one-dimensional Anderson model ($a\to\infty$), in which all states are localized and the localization length is minimal at the band edge, the long-range model with $1

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.25806

Authors: Bahovadinov, Murod S., Jalolov, Faridun N., Kravtsov, Vladimir E., Altshuler, Boris L., Shlyapnikov, Georgy V.

Institutions: National Research University Higher School of Economics, Russian Quantum Center, Skolkovo Institute of Science and Technology, The Abdus Salam International Centre for Theoretical Physics (ICTP), Columbia University

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Russian Science Foundation, National Research University Higher School of Economics

OpenAlex ID: W7204460893

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