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

Understand

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.