From the pseudogap metal to the Fermi liquid using ancilla qubits

Abstract

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 two ancilla qubits per square lattice site, and employ them to obtain a variational wave function of a fractionalized Fermi liquid for the pseudogap metal state. We propose a multilayer Hamiltonian 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.