Singular order parameter interaction at nematic quantum critical point in two dimensional electron systems

TL;DR

This paper investigates the complex infrared behavior of N-point interactions in two-dimensional quantum critical electron systems with nematic order, revealing their singular and marginal nature which challenges finite-order truncations.

Contribution

It demonstrates that all N-point interactions are singular and marginal at the nematic quantum critical point, invalidating finite-order truncations of the effective action.

Findings

N-point interactions diverge for N ≥ 4 in the static collinear limit

Interactions exhibit singular momentum and energy dependence

Finite-order truncations of the effective action are not justified

Abstract

We analyze the infrared behavior of effective N-point interactions between order parameter fluctuations for nematic and other quantum critical electron systems with a scalar order parameter in two dimensions. The interactions exhibit a singular momentum and energy dependence and thus cannot be represented by local vertices. They diverge for all N greater or equal 4 in a collinear static limit, where energy variables scale to zero faster than momenta, and momenta become increasingly collinear. The degree of divergence is not reduced by any cancellations and renders all N-point interactions marginal. A truncation of the order parameter action at quartic or any other finite order is therefore not justified. The same conclusion can be drawn for the effective action describing fermions coupled to a U(1) gauge field in two dimensions.