Microscopic Emergence of Ancilla Lattice Physics in the Emery Model

We derive a controlled low-energy effective theory for the three-band Emery model on the Lieb lattice near (n=2) filling. Starting from the positive charge-transfer regime, a sequence of Schrieffer--Wolff transformations rigorously establishes a direct microscopic mapping onto an ancillary lattice structure. For realistic cuprate-like parameters, this framework naturally reproduces the conventional Fermi-liquid (FL) phase at a filling shifted by one electron per site. Our analysis identifies the precise microscopic conditions required to access the exotic fractionalized Fermi-liquid (FL$^*$) phase. We show that realizing FL$^*$ requires nonstandard cuprate parameter regimes together with additional interactions that stabilize a quantum spin liquid in the background ancilla layer. These results establish a microscopic foundation for ancilla physics in multiorbital materials and clarify the conditions for realizing FL$^*$. We discuss the possibility to replicate ancilla model physics in Lieb lattice cold atom simulations.