  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. Second, we introduce an RG based classification
scheme and give a detailed argument that all phases within the classification
scheme obey the area law. Third, we define a special sub-class of gapped
phases, \textit{topological quantum liquids}, which captures all examples of
current physical relevance, and we rigorously show that TQLs obey an area law.
Fourth, we show that all topological quantum liquids have MERA representations
which achieve unit overlap with the ground state in the thermodynamic limit and
which have a bond dimension scaling with system size $L$ as $e^{c
\log^{d(1+\delta)}(L)}$ for all $\delta >0$. For example, we show that chiral
phases in $d=2$ dimensions have an approximate MERA with bond dimension $e^{c
\log^{2(1+\delta)}(L)}$. We discuss extensively a number of subsidiary ideas
and results necessary to make the main arguments, including field theory
constructions. While our argument for the general area law rests on
physically-motived assumptions (which we make explicit) and is therefore not
rigorous, we may conclude that "conventional" gapped phases obey the area law
and that any gapped phase which violates the area law must be a dragon.
