Topological and Entanglement Properties of Resonating Valence Bond wavefunctions

Understand

We examine in details the connections between topological and entanglement properties of short-range resonating valence bond (RVB) wave functions using Projected Entangled Pair States (PEPS) on kagome and square lattices on (quasi-)infinite cylinders with generalized boundary conditions (and perimeters with up to 20 lattice spacings).

• Making use of disconnected topological sectors in the space of dimer lattice coverings, we explicitly derive (orthogonal) "minimally entangled" PEPS RVB states.
• For the kagome lattice, we obtain, using the quantum Heisenberg antiferromagnet as a reference model, the finite size scaling of the energy separations between these states.
• In particular, we extract two separate (vanishing) energy scales corresponding (i) to insert a vison line between the two ends of the cylinder and (ii) to pull out and freeze a spin at either end.