Symmetric inseparability and number entanglement in charge conserving mixed states

TL;DR

This paper investigates conditions for inseparability in charge-conserving mixed states, introducing number entanglement as a witness and entanglement monotone, with analysis in thermal 1D systems.

Contribution

It introduces number entanglement as a new measure for symmetric inseparability and demonstrates its effectiveness and scaling in thermal 1D systems.

Findings

Number entanglement detects inseparable charge sectors.

Number entanglement is an entanglement monotone.

Scaling of number entanglement analyzed in thermal 1D systems.

Abstract

We explore sufficient conditions for inseparability in mixed states with a globally conserved charge, such as a particle number. We argue that even separable states may contain entanglement in fixed charge sectors, as long as the state can not be separated into charge conserving components. As a witness of symmetric inseparability we study the number entanglement (NE), $\Delta S_m$, defined as the entropy change due to a subsystem's charge measurement. Whenever $\Delta S_m > 0$, there exist inseparable charge sectors, having finite (logarithmic) negativity, even when the full state is either separable or has vanishing negativity. We demonstrate that the NE is not only a witness of symmetric inseparability, but also an entanglement monotone. Finally, we study the scaling of $\Delta S_m$ in thermal 1D systems combining high temperature expansion and conformal field theory.