香蕉视频

PHYSICS SEMINAR

Title:聽Entanglement and separability of Rokhsar-Kivelson and resonating valence-bond states

础产蝉迟谤补肠迟:听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, we 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 disconnected subsystems, implying the absence of entanglement between the subsystems. For RVB states, we show separability for disconnected subsystems up to exponentially small terms in the distance d between the two 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 R茅nyi-1/2 entropy in the limit of complementary subsystems.
Based on joint work with Cl茅ment Berthier and William Witczak-Krempa, arXiv: 2212.11740

CRM-Salle 4336-4384, Pav. Andr茅 Aisenstadt