Bound entanglement in quantum phase transitions

Entanglement as a crucial ingredient of quantum many-body systems has different forms, such as free entanglement and bound entanglement. In this study we show that, like free entanglement, bound entanglement can also induce quantum phase transitions. 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.