Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 53, Issue 4, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8121/ab5eb8
Keywords
Anderson localization; imaginary random potential; band-center anomaly; non-Hermitian Hamiltonian; complex systems; disordered systems
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Funding
- Vietnam National Foundation for Science and Technology Development (NAFOSTED) [103.01-2018.05]
- National Research Foundation of Korea - Korean Government [NRF-2019R1F1A1059024]
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We study numerically the localization properties of eigenstates in a one-dimensional random lattice described by a non-Hermitian disordered Hamiltonian, where both the disorder and the non-Hermiticity are inserted simultaneously in the on-site potential. We calculate the averaged participation number, the Shannon entropy and the structural entropy as a function of other parameters. We show that, in the presence of an imaginary random potential, all eigenstates are localized in the thermodynamic limit and strong anomalous Anderson localization occurs at the band center. In contrast to the usual localization anomalies where a weaker localization is observed, the localization of the eigenstates near the band center is strongly enhanced in the present non-Hermitian model. This phenomenon is associated with the occurrence of a large number of strongly-localized states with pure imaginary energy eigenvalues.
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