From the pseudogap metal to the Fermi liquid using ancilla qubits

We propose a new parton theory of the hole-doped cuprates, describing the evolution from the pseudogap metal with small Fermi surfaces to the conventional Fermi liquid with a large Fermi surface. We introduce 2 ancilla qubits per square lattice site, and employ them to obtain a variational wavefunction of a fractionalized Fermi liquid for the pseudogap metal state. We propose a multi-layer Hamiltonion for the cuprates, with the electrons residing in the 'physical' layer, and the ancilla qubits in two 'hidden' layers: the hidden layers can be decoupled from the physical layer by a canonical transformation which leaves the hidden layers in a trivial gapped state. This Hamiltonian yields an emergent gauge theory which describes not only the fractionalized Fermi liquid, but also the conventional Fermi liquid, and possible exotic intermediate phases and critical points. The fractionalized Fermi liquid has hole pockets with quasiparticle weight which is large only on "Fermi arcs", and fermionic spinon excitations which carry charges of the emergent gauge fields.