Abstract
Expanding on the zipper entanglement renormalization (ZER) framework proposed for two-dimensional (2D) chiral topological order, in this thesis we discuss how to incorporate insights from Fermi liquid entanglement structures to perform renormalization on states with a Fermi surface. By treating the 2D free-fermion metallic input state as a combination of self-similar metallic sub-systems and one-dimensional metallic states in different orientations, ZER can accommodate the logarithmic entanglement entropy scaling of L log L, where L denotes the linear size of the sub-system. Numerical computations on a 2D tight-binding model validate the methodology in handling metallic states, indicating its potential for treating highly-entangled quantum many-body states like Fermi liquids.