Critical quantum liquids and the cuprate high temperature superconductors

We present a theoretical framework for the cuprate superconductors, rooted in a fractionalized Fermi liquid (FL*) description of the intermediate-temperature pseudogap phase at low doping. The FL* theory predicted hole pockets each of fractional area $p/8$ at hole doping p, in contrast to the area $p/4$ in a spin density wave state or its thermal fluctuation. A recent magnetotransport observation of the Yamaji angle is in good agreement with area $p/8$. We review a theory for the FL* phase of a single-band model using a layer construction with a pair of ancilla qubits on each site: the Ancilla Layer Model (ALM). Its mean field yields hole pockets of area $p/8$, and matches the gapped photoemission spectrum in the anti-nodal region of the Brillouin zone. Fluctuations are described by the SU(2) gauge theory of a background spin liquid with critical Dirac spinons. A Monte Carlo study of the thermal SU(2) gauge theory transforms the hole pockets into Fermi arcs in photoemission. One route to confinement of FL* upon lowering temperature yields a d-wave superconductor via a Kosterlitz-Thouless transition of $h/(2e)$ vortices, with nodal Bogoliubov quasiparticles featuring anisotropic velocities and vortices surrounded by charge order halos. An alternative route produces a charge-ordered metallic state that exhibits quantum oscillations in agreement with experiments. Increasing doping from the FL* phase in the ALM drives a transition to a Fermi liquid at large doping, passing through an intermediate strange metal regime. We formulate a theory of this metal using a critical quantum `charge' liquid of mobile electrons in the presence of disorder, via an extension of the Sachdev-Ye-Kitaev model. At low temperatures, and across optimal and over doping, we address the regimes of extended non-Fermi liquid behavior by Griffiths effects near quantum phase transitions in disordered metals.