Quantum phase transitions of metals in two spatial dimensions: I. Ising-nematic order

TL;DR

This paper develops a renormalization group framework for understanding the quantum phase transition to Ising-nematic order in two-dimensional metals, revealing complex critical behavior and scaling properties.

Contribution

It introduces a set of local field theories for the quantum critical point, incorporating compatibility constraints and extending to related symmetry-breaking transitions.

Findings

Scaling forms for response functions are proposed.

Three-loop computations support the theoretical framework.

Results extend to Fermi surfaces coupled to gauge fields.

Abstract

We present a renormalization group theory for the onset of Ising-nematic order in a Fermi liquid in two spatial dimensions. This is a quantum phase transition, driven by electron interactions, which spontaneously reduces the point-group symmetry from square to rectangular. The critical point is described by an infinite set of 2+1 dimensional local field theories, labeled by points on the Fermi surface. Each field theory contains a real scalar field representing the Ising order parameter, and fermionic fields representing a time-reversed pair of patches on the Fermi surface. We demonstrate that the field theories obey compatibility constraints required by our redundant representation of the underlying degrees of freedom. Scaling forms for the response functions are proposed, and supported by computations by up to three loops. Extensions of our results to other transitions of two-dimensional Fermi liquids with broken point-group and/or time-reversal symmetry are noted. Our results extend also to the problem of a Fermi surface coupled to a U(1) gauge field.