Renormalization group constructions of topological quantum liquids and beyond

Understand

We give a detailed physical argument for the area law for entanglement entropy in gapped phases of matter arising from local Hamiltonians.

• Our approach is based on renormalization group (RG) ideas and takes a resource oriented perspective.
• We report four main results.
• First, we argue for the "weak area law": any gapped phase with a unique ground state on every closed manifold obeys the area law.