The foot, the fan, and the cuprate phase diagram: Fermi-volume-changing quantum phase transitions (2501.16417v8)

Abstract: A Fermi liquid with a 'large' Fermi surface (FL) can have a quantum phase transition to a spin density wave state (SDW) with reconstructed 'small' Fermi pockets. Both FL and SDW phases obey the Luttinger constraints on the volume enclosed by the Fermi surfaces. Critical spin fluctuations lead to spin-singlet $d$-wave pairing, as observed in the cuprates. Studies of the influence of spatial disorder on the FL-SDW quantum phase transition predict an extended quantum-critical Griffiths-type phase at low temperatures on the large Fermi surface side. These computations agree with the 'foot' of strange metal transport, and recent low temperature neutron scattering observations on La$_{2-x}$Sr$_x$CuO$_4$. However, this theory cannot explain the higher temperature pseudogap and the 'fan' of strange metal behavior of the hole-doped cuprates. Here we need to consider underlying Fermi-volume-changing quantum phase transitions without symmetry breaking. Then the small Fermi surface phase does not obey the Luttinger constraint, and the pseudogap metal is described by thermal fluctuations above a 'fractionalized Fermi liquid' (FL*) or a 'holon metal', with the descriptions related by a duality on a background spin liquid. The quantum critical fan is described using a field theory for an underlying FL-FL* quantum phase transition in the presence of spatial disorder. This field theory can be mapped to a form which can be analyzed using the methods of the Sachdev-Ye-Kitaev model. Such an analysis successfully models linear-in-temperature resistivity, optical conductivity and thermopower observations in the quantum critical fan. The confinement crossover connecting these lower and higher temperature descriptions is also discussed.