Generalized Hertz action and quantum criticality of two-dimensional Fermi systems

TL;DR

This paper develops a generalized Hertz action for two-dimensional Fermi systems with zero wavevector, clarifies the quantum critical scaling behavior, and explains Monte Carlo results related to electronic nematic quantum criticality.

Contribution

It introduces a generalized Hertz action free from singular interactions and highlights the importance of a scale-dependent ordering wavevector in RG analysis.

Findings

Generalized Hertz action avoiding singularities

Quantum critical scaling dominated by z≈2 regime

Explanation of Monte Carlo results for nematic criticality

Abstract

We reassess the structure of the effective action and quantum critical singularities of two-dimensional Fermi systems characterized by the ordering wavevector $\vec{Q}= \vec{0}$. By employing infrared cutoffs on all the massless degrees of freedom, we derive a generalized form of the Hertz action, which does not suffer from problems of singular effective interactions. We demonstrate that the Wilsonian momentum-shell renormalization group (RG) theory capturing the infrared scaling should be formulated keeping $\vec{Q}$ as a flowing, scale-dependent quantity. At the quantum critical point, scaling controlled by the dynamical exponent $z=3$ is overshadowed by a broad scaling regime characterized by a lower value of $z \approx 2$. This in particular offers an explanation of the results of quantum Monte Carlo simulations pertinent to the electronic nematic quantum critical point.