Study of two-spin entanglement in singlet states

• Studied entanglement properties of a two-spin subsystem in spin-singlets.
• In a singlet, homogenization maximizes entanglement of two spins with the rest.
• A new class of resonating-valence-bond states is proposed.
• Proposed states are ground states of an infinite-range Heisenberg model.

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, Ev2 (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 Ev2 rapidly increases with system size and saturates at its maximum allowed value. We adopt two ways of obtaining maximal Ev2 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 E2v states represent a new class of resonating-valence-bond states which we show to be the ground states of the infinite-range Heisenberg model.