Symplectic entanglement II: spin networks

Eastern Gravity Meeting, Rochester Institute of Technology

One of the open problems in Loop Quantum Gravity is finding semi-classical states describing classical geometries with quantum corrections. Such semi-classical states are expected to be highly entangled in order to match perturbative results for the graviton correlations. In this talk, we present a new class of entangled spin network states that are labeled by symplectic matrices and are generated by squeezing the Ashtekar-Lewandowski vacuum. We show that the entanglement entropy between a subgraph and its complement can be calculated analytically as a function of the symplectic matrix labelling the state. Projecting these states onto the kinematical Hilbert space provides a new candidate for highly entangled semi-classical states. This talk is based on work with Eugenio Bianchi & Nelson Yokomizo.