Bound entanglement in quantum phase transitions

TL;DR

This paper explores quantum phase transitions involving changes in entanglement types, introducing a method to construct Hamiltonians with specific entanglement properties in spin chains.

Contribution

It presents a reverse construction method for Hamiltonians exhibiting bound entanglement transitions, advancing understanding of quantum criticality in spin systems.

Findings

Constructed Hamiltonians with bound entanglement transitions

Demonstrated examples of entanglement type change at quantum critical points

Provided a theoretical framework for entanglement-based quantum phase transitions

Abstract

We investigate quantum phase transitions in which a change in the type of entanglement from bound entanglement to either free entanglement or separability may occur. In particular, we present a theoretical method to construct a class of quantum spin-chain Hamiltonians that exhibit this type of quantum criticality. Given parameter-dependent two-site reduced density matrices (with prescribed entanglement properties), we lay out a reverse construction for a compatible pure state for the whole system, as well as a class of Hamiltonians for which this pure state is a ground state. This construction is illustrated through several examples.