A novel quantum Shannon entropy as a sensitivity of Anderson transitions: It simultaneously relates to periodic and antiperiodic boundary conditions

作者：Gong, Longyan^*; Zhang, Jingjing; Ma, Kaixin; Zhou, Xingfei; Zhai, Xuechao; Cheng, Weiwen; Zhao, Shengmei

来源：EPL, 2018, 122(3): 37002.

DOI：10.1209/0295-5075/122/37002

• SCALING THEORY
• LOCALIZATION
• ABSENCE
• DIFFUSION
• MODEL

In general, extended states are more sensitive to boundary conditions (BCs) than localized ones. We expand an eigenstate vertical bar beta(p)> of a Hamiltonian with periodic BC as the superposition of all eigenstates vertical bar beta(a)> of the same Hamiltonian but with antiperiodic BC, i.e., vertical bar beta(p)> = Sigma(N)(beta a=1)vertical bar beta(a)> <beta(a)vertical bar beta(p)> = Sigma(N)(beta a=1) C-beta a vertical bar beta(a)>, where C-beta a = <beta(a)vertical bar beta(p)> and N is the Hilbert space dimension. Thus, we propose a novel quantum Shannon entropy S-b = -Sigma(N)(beta a=1)vertical bar C-beta a vertical bar(2) log vertical bar C-beta a vertical bar(2), which simultaneously relates to periodic and antiperiodic BCs. It measures the information of vertical bar beta(p)> contained in all the N eigenstates vertical bar beta(a)>. Based on it, we define a reduced quantum Shannon entropy S-b(r) = 1 - S-b/log N, where 0 <= S-b(r) <= 1. We apply it to several typical models. Results show that < S-b(r)> 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 < S-b(r)> around Anderson transition points. Therefore, S-b(r) can be used as a sensitivity measure to characterize Anderson transitions.

• 出版日期2018-5
• 单位南京邮电大学