Entanglement and Quantum phase transition in topological insulators

TL;DR

This paper investigates entanglement properties in topological insulators, revealing distinct entanglement structures in surface and bulk states, and proposes a method to detect entanglement experimentally.

Contribution

It demonstrates the presence of different entanglement structures in surface and bulk states of topological insulators and suggests a practical detection scheme.

Findings

Surface states are maximally entangled in a 4D subspace.

Bulk states are entangled in the entire Hilbert space.

A detection scheme using measurement and quantum gates is proposed.

Abstract

Presence of entangled states is explicitly shown in Topological insulator (TI) $Bi_2Te_3$. The surface and bulk state are found to have the different structures of entanglement. The surface states live as maximally entangled states in the 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 z-direction. Scheme to detect entanglement in a 2-D model using measurement, confirming natural implementation of universal Hadamard with Controlled-NOT gates is explicated.