Rényi–Fisher entropy product as a marker of topological phase transitions

Abstract

The combined Rényi-Fisher entropy product of electrons plus holes displays a minimum at the charge neutrality points. The Stam-Rényi difference and the Stam-Rényi uncertainty product of the electrons plus holes, show maxima at the charge neutrality points. Topological quantum numbers capable of detecting the topological insulator and the band insulator phases, are defined. Upper and lower bounds for the position and momentum space Rényi-Fisher entropy products are derived.

Benchmark calculations of Rényi, Tsallis entropies, and Onicescu information energy for ground state helium using correlated Hylleraas wave functions

“…In addition, Tsallis statistics emerges in several systems of ultracold atoms . Furthermore, these quantities provide different perspectives to statistic mechanics, entropic uncertainty relations, electron correlation, orbital‐free density functional theory (DFT), and other applications …”

“…[16][17][18][19] Furthermore, these quantities provide different perspectives to statistic mechanics, [20][21][22][23][24][25][26] entropic uncertainty relations, [27][28][29] electron correlation, [30][31][32][33][34][35][36][37][38][39][40][41] orbital-free density functional theory (DFT), [42,43] and other applications. [44][45][46][47][48][49][50][51][52][53][54] In particular, by treating the electron density as a continuous probability distribution, these quantities are naturally extended to the position space and applied to numerous types of potential [55][56][57][58][59][60][61] and atomic and molecular systems. [30][31]…”

Rényi’s divergence as a chemical similarity criterion

“…Considering a historical point of view, perhaps Rényi's work can be considered the first attempt to generalize Shannon's entropy. Since the 1990s, Rényi's entropy has been profusely used in the field of atomic and molecular physics [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], and these works were focused on the study of the electron correlation phenomenon.…”

Fisher Information of Free-Electron Landau States

“…Although the information quantity itself has not been a major concern in the literature of solid-state physics, some recent works relate the information concept and the quantum number n that specifies the Landau levels under fixed electric and magnetic fields [18][19][20]. The aim of these studies is to propose an indicator of topological phase transitions in twodimensional topological insulators, and the behavior of Fisher information and the Rényi-Fisher entropy product have been studied for eigenstates in 2D gapped Dirac materials for several values of n. Contrary to the Landau states in this study, the eigenstate wavefunctions have no dependence on the azimuthal quantum number.…”