Study of two-spin entanglement in singlet states

TL;DR

This paper investigates entanglement in two-spin subsystems within singlet states, revealing how to maximize different entanglement measures and constructing highly entangled states that serve as ground states for the infinite-range Heisenberg model.

Contribution

It introduces methods to maximize entanglement measures in singlet states and constructs new highly entangled resonating-valence-bond states as ground states.

Findings

Maximized average two-spin entanglement in a single VB state.

Maximized subsystem-to-rest entanglement ($E_v^2$) through superpositions.

Constructed explicit four- and six-spin highly entangled states.

Abstract

We study the entanglement properties of two-spin subsystems in spin-singlet states. The average entanglement between two spins is maximized in a single valence-bond (VB) state. On the other hand, $E_v^2$ (the average entanglement between a subsystem of two spins and the rest of the system) can be maximized through a homogenized superposition of the VB states. The maximal $E_v^2$ rapidly increases with system size and saturates at its maximum allowed value. We adopt two ways of obtaining maximal $E_v^2$ states: (1) imposing homogeneity on singlet states; and (2) generating isotropy in a general homogeneous state. By using these two approaches, we construct explicitly four-spin and six-spin highly entangled states that are both isotropic and homogeneous. Our maximal $E^2_v$ states represent a new class of resonating-valence-bond states which we show to be the ground states of the infinite-range Heisenberg model.