Entanglement entropy and entanglement spectrum of Bi_1−xSb_x(1 1 1) bilayers

Abstract

We study topological properties of Bi$_{1-x}$Sb$_{x}$ bilayers in the (111) plane using entanglement measures. Electronic structures are investigated within multi-orbital tight-binding model and structural stability is confirmed through first-principles calculations. Topologically non-trivial nature of bismuth bilayer is proved by the presence of spectral flow in the entanglement spectrum. We consider topological phase transitions driven by a composition change x, an applied external electric field in Bi bilayer and strain in Sb bilayer. Composition- and strain-induced phase transitions reveal a finite discontinuity in the entanglement entropy. This quantity remains a continuous function of the electric field strength, but shows a finite discontinuity in the first derivative. We relate the difference in behavior of the entanglement entropy to the breaking of inversion symmetry in the last case.

Elastic, mechanical, and thermodynamic properties of Bi-Sb binaries: Effect of spin-orbit coupling

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DMRG and Monte Carlo studies of $\textrm{CrI}_3$ magnetic phases and the phase transition

“…In recent years, the wide class of two-dimensional van der Waals crystals, which includes semiconductors, superconductors, semi-metals, topological insulators, charge density waves materials and ferroelectrics, has been extensively studied both by theoretical and experimental methods [1,2,3,4,5,6,7,8,9,10,11,12]. These materials have many potential applications in novel approaches towards electronics, like spintronics, valleytronics, and optoelectronics [3,13,14,15,16,17].…”

Deep learning for disordered topological insulators through their entanglement spectrum

“…For time-reversal topological insulators, on the other hand, much less has been reported in this regard, with the exception of a variant of the Bott index which enables a real-space study of the Z 2 number [16] or a spin Bott index [18] in analogy with the spin Chern number [19]. Some quantities that have been shown to be related to the topology of the system are the entanglement spectrum and entropy [20][21][22][23][24][25][26][27][28][29][30][31]. These magnitudes measure the degree of entanglement of our ground state between two halves of the system.…”