Laboratoire de Physique Théorique
Toulouse - UMR 5152

Entanglement and separability are two opposite yet intertwined notions in quantum mechanics. A quantum state is said to be entangled if it is not separable, and vice versa. Quantifying how entangled two subsystems are remains a challenging problem, which has led to important insights in the context of quantum many-body systems. In this talk, I will discuss entanglement and separability of dimer Rokhsar-Kivelson (RK) states and resonating valence-bond (RVB) states. For dimer RK states on general tilable graphs, we prove the exact separability of the reduced density matrix of two or more disconnected subsystems, implying the absence of entanglement between the subsystems. For RVB states, we show separability for disconnected systems up to exponentially small terms in the distance d between the subsystems. We argue that separability does hold in the scaling limit, even for arbitrarily small ratio d/L, where L is the characteristic size of the subsystems. Our results hold irrespective of the underlying graph (which include square and triangular lattices), and hence suggest that separability (up to exponentially small terms) between disjoint regions is a universal feature of RVB states. In the case of adjacent subsystems for the RK states, we derive exact results for the logarithmic negativity in terms of partition functions of the underlying statistical model, and recover the known result for the Rényi-1/2 entropy in the limit of complementary subsystems.

Based on joint work with Clément Berthier and William Witczak-Krempa, arXiv : 2212.11740.