On the Nature of Infrared Singularities in $d\leq 2$ Disordered Interacting Systems

TL;DR

This paper investigates infrared singularities in disordered interacting systems in low dimensions, revealing instabilities and soft modes that challenge conventional analysis methods.

Contribution

It identifies sample-specific instabilities and soft modes in disordered systems, proposing the optimal fluctuation method to evaluate their probabilities.

Findings

Linear instability in the spin triplet channel.

Accumulation of soft modes in the density-density channel.

Instability of the weak-interacting fixed point.

Abstract

We address the problem of infrared singularities in the perturbation theory for disordered interacting systems in $d\leq 2$. We show that a typical, sufficiently large interacting system exhibits a linear instability in the spin triplet channel. In a density-density channel, although stability is preserved, a large number of soft modes is accumulated. These phenomena are responsible for the instability of the weak-interacting fixed point. Although generic, the unstable direction and soft modes are highly sample specific and can not be effectively captured by conventional techniques based on an averaging procedure. Rather, the instability is determined by the largest eigenvalues of the polarization operator. We propose to employ the optimal fluctuation method for evaluating the probability of such events.