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arXiv:2501.16417 · Physica C Superconductivity

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

Subir Sachdev A

Published Apr 9, 2025• 11 citations
arXivHTMLPDF
DOI
10.1016/j.physc.2025.1354707

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Quantum phase transitions of metals involve changes in the Fermi surface, and can be divided into three categories. The first two categories involve symmetry breaking, and lead to a deformation or reconstruction of the Fermi surface. The third category involves a change in the volume enclosed by the Fermi surface without any symmetry breaking: one phase is a Fermi liquid (FL) with the conventional Luttinger volume, while the other phase is a `fractionalized Fermi liquid' (FL*), which has a non-Luttinger volume Fermi surface accompanied by a spin liquid with fractionalized excitations. It is a relatively simple matter to obtain a FL*-FL transition in Kondo lattice models. However, the FL*-FL transition can also be present in single-band Hubbard-like models: this is efficiently described by the `ancilla' method, which shows that the transition is a `flipped' Kondo lattice transition. This single-band FL*-FL transition is argued to apply to the metallic states of the hole-doped cuprates. In the clean limit, the critical properties of the quantum transitions in the three categories are distinct, but all lead to perfect metal transport in the quantum-critical regime. Impurity-induced `Harris disorder', with spatial fluctuations in the local position of the quantum critical point, is a relevant perturbation to the clean critical points. In the presence of Harris disorder, all three categories exhibit strange metal behavior, which can be described by a universal two-dimensional Yukawa-Sachdev-Ye-Kitaev model.

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We consider the two-dimensional $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model with the Fermi level being close to Van Hove singularities. The phase diagram of the model is discussed. Far from the quantum phase transition (QPT) into ferro- (antiferro-) magnetic states, the self-energy at the singularity points has a nearly linear energy dependence, the density of states being proportional to ${\mathrm{ln}}^{3}|\ensuremath{\varepsilon}|.$ In the quantum-disordered and quantum-critical regimes near the QPT a scaling approach is used. At small energies the self-energy demonstrates a powerlike behavior with the exponent changing from unity to zero in a narrow energy interval. Provided that the system is close to ferromagnetic instability which occurs at ${t}^{\ensuremath{'}}/\stackrel{\ensuremath{\rightarrow}}{t}\ensuremath{-}1/2,$ the quasiparticle spectral weight has, instead of a narrow peak, a broad maximum and is nonmonotonous at small energies. The application of the results to cuprates is discussed.

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The phase diagram of the superconducting cuprates is a manifestation of quantum phase transition (QPT). There is still controversy if the quantum fluctuations generating the pseudogap region is a precursor to the superconducting region or they are competing phases. By modelling the basic possible Hamiltonian for this class of materials as a nonlinear dynamic system, using doping as the tuning parameter, it is possible to obtain a visualized phase diagram which captures fairly the phase diagram of the superconducting cuprates. The numerical results depict that as we doped from slight to optimal, there are three quantum critical points (QCPs): the first at the QPT from the Mott insulator and antiferromagnetic (AFM) phase to the pseudogap at slight doping, the second at the QPT from the pseudogap to the superconducting phase at minimum doping and the third is a hidden QPT due to collapse of the pseudogap around optimal doping. Therefore, the results obtained here in the context of nonlinear dynamic visualization shed new light on the study of the phase diagram of the high TC superconducting cuprates.

International Journal of Theoretical and Mathematical Physics•Jan 1, 2014•0 citations
Quantum phase transitions of metals involve changes in the Fermi surface, and can be divided into three categories. The first two categories involve symmetry breaking, and lead to a deformation or reconstruction of the Fermi surface. The third category involves a change in the volume enclosed by the Fermi surface without any symmetry breaking: one phase is a Fermi liquid (FL) with the conventional Luttinger volume, while the other phase is a `fractionalized Fermi liquid' (FL*), which has a non-Luttinger volume Fermi surface accompanied by a spin liquid with fractionalized excitations. It is a relatively simple matter to obtain a FL*-FL transition in Kondo lattice models. However, the FL*-FL transition can also be present in single-band Hubbard-like models: this is efficiently described by the `ancilla' method, which shows that the transition is a `flipped' Kondo lattice transition. This single-band FL*-FL transition is argued to apply to the metallic states of the hole-doped cuprates. In the clean limit, the critical properties of the quantum transitions in the three categories are distinct, but all lead to perfect metal transport in the quantum-critical regime. Impurity-induced `Harris disorder', with spatial fluctuations in the local position of the quantum critical point, is a relevant perturbation to the clean critical points. In the presence of Harris disorder, all three categories exhibit strange metal behavior, which can be described by a universal two-dimensional Yukawa-Sachdev-Ye-Kitaev model.
We consider the two-dimensional $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model with the Fermi level being close to Van Hove singularities. The phase diagram of the model is discussed. Far from the quantum phase transition (QPT) into ferro- (antiferro-) magnetic states, the self-energy at the singularity points has a nearly linear energy dependence, the density of states being proportional to ${\mathrm{ln}}^{3}|\ensuremath{\varepsilon}|.$ In the quantum-disordered and quantum-critical regimes near the QPT a scaling approach is used. At small energies the self-energy demonstrates a powerlike behavior with the exponent changing from unity to zero in a narrow energy interval. Provided that the system is close to ferromagnetic instability which occurs at ${t}^{\ensuremath{'}}/\stackrel{\ensuremath{\rightarrow}}{t}\ensuremath{-}1/2,$ the quasiparticle spectral weight has, instead of a narrow peak, a broad maximum and is nonmonotonous at small energies. The application of the results to cuprates is discussed.
The phase diagram of the superconducting cuprates is a manifestation of quantum phase transition (QPT). There is still controversy if the quantum fluctuations generating the pseudogap region is a precursor to the superconducting region or they are competing phases. By modelling the basic possible Hamiltonian for this class of materials as a nonlinear dynamic system, using doping as the tuning parameter, it is possible to obtain a visualized phase diagram which captures fairly the phase diagram of the superconducting cuprates. The numerical results depict that as we doped from slight to optimal, there are three quantum critical points (QCPs): the first at the QPT from the Mott insulator and antiferromagnetic (AFM) phase to the pseudogap at slight doping, the second at the QPT from the pseudogap to the superconducting phase at minimum doping and the third is a hidden QPT due to collapse of the pseudogap around optimal doping. Therefore, the results obtained here in the context of nonlinear dynamic visualization shed new light on the study of the phase diagram of the high TC superconducting cuprates.