Lectures on the quantum phase transitions of metals

TL;DR

This paper reviews quantum phase transitions in metals, focusing on symmetry-breaking and non-symmetry-breaking types, including the novel FL* phase, and discusses their critical properties and effects of disorder.

Contribution

It introduces the FL* phase and its transition mechanisms in single-band models, connecting them to experimental observations in cuprates and analyzing disorder effects.

Findings

FL* phase involves non-Luttinger Fermi surface with fractionalized excitations.

Distinct critical behaviors for different transition categories in clean systems.

Disorder induces strange metal behavior described by a Yukawa-Sachdev-Ye-Kitaev model.

Abstract

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.