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

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.

43 pages, 15 figures; Contribution to the memorial volume for Jan Zaanen; Expanded discussion on evidence for fractionalization in the pseudogap, and its consequences; Added reference to arXiv:2411.10631, arguing their Yamaji effect observations support the FL* pseudogap metal; (v8) Added figure of FL* Fermi surfaces from cond-mat/0702119

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Cited by in corpus (9)

• Extended strange metal regime from superconducting puddles
• Fractionalized Fermi liquids and the cuprate phase diagram
• Canted magnetism and ${\mathbb{Z}}_2$ fractionalization in metallic states of the Lieb lattice Hubbard model near quarter filling
• Functional renormalization group for extremely correlated electrons
• Thermopower across Fermi-volume-changing quantum phase transitions without translational symmetry breaking
• Pseudogap and strange metal states in the square-lattice Hubbard model: A comprehensive study
• Critical spin fluctuations across the superconducting dome in La${}_{2-x}$Sr${}_x$CuO${}_4$
• Pseudogap in electron-doped cuprates: thermal precursor to magnetism
• Strain-induced structural change and nearly-commensurate diffuse scattering in the model high-temperature superconductor HgBa${}_2$CuO${}_{4+\delta }$