Entanglement and quantum phase transition in topological insulators

Abstract

Presence of entangled states is explicitly shown in a topological insulator (TI) [Formula: see text]. The surface and bulk state are found to have different structures of entanglement. The surface states live as maximally entangled states in a four-dimensional subspace of total Hilbert space (spin, orbital, space). However, bulk states are entangled in the whole Hilbert space. Bulk states are found to be entangled maximally by controlled injection of electrons with momentum only along the [Formula: see text]-direction. At quantum phase transition (QPT) point, both states become maximally entangled two qubit states.