Volume 122, Number 3, May 2018
|Number of page(s)||6|
|Section||Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties|
|Published online||27 June 2018|
A novel quantum Shannon entropy as a sensitivity of Anderson transitions: It simultaneously relates to periodic and antiperiodic boundary conditions
1 Department of Applied Physics, Nanjing University of Posts and Telecommunications - Nanjing, 210003, China
2 Institute of Signal Processing and Transmission, Nanjing University of Posts and Telecommunications Nanjing, 210003, China
3 New Energy Technology Engineering Laboratory of Jiangsu Province, Nanjing University of Posts and Telecommunications - Nanjing, 210003, China
Received: 23 March 2018
Accepted: 31 May 2018
In general, extended states are more sensitive to boundary conditions (BCs) than localized ones. We expand an eigenstate of a Hamiltonian with periodic BC as the superposition of all eigenstates of the same Hamiltonian but with antiperiodic BC, i.e., , where and N is the Hilbert space dimension. Thus, we propose a novel quantum Shannon entropy , which simultaneously relates to periodic and antiperiodic BCs. It measures the information of contained in all the N eigenstates . Based on it, we define a reduced quantum Shannon entropy , where . We apply it to several typical models. Results show that are relatively smaller for delocalized states and are less than and close to one for localized states as N increases. There are rapid changes in around Anderson transition points. Therefore, can be used as a sensitivity measure to characterize Anderson transitions.
PACS: 72.15.Rn – Localization effects (Anderson or weak localization) / 71.23.An – Theories and models; localized states / 71.30.+h – Metal-insulator transitions and other electronic transitions
© EPLA, 2018
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