Renormalization group and stability in the exciton Bose liquid

Abstract

The exciton Bose liquid (EBL) is a hypothesized phase of bosons in $2+1\text{D}$ which possesses a dispersion that is gapless along the coordinate axes in momentum space. The low energy theory of the EBL involves modes on all length scales, extending all the way down to the lattice spacing. In this paper, we discuss a renormalization group scheme that can be used to address the stability of this and related phases of matter. We find that, in the absence of an extensively large symmetry group, realizing the simplest formulation of the EBL always requires fine-tuning. However, we also argue that the addition of certain marginal interactions can be used to realize a stable phase, without the need for fine-tuning. A simple generalization to $3+1\text{D}$ is also discussed.