Infinite critical boson induced non-Fermi liquid in $d=3-\epsilon$ dimensions

TL;DR

This paper investigates a novel non-Fermi liquid phase induced by an infinite set of critical bosons on a sphere in a fermion-boson system near a quantum phase transition in three dimensions.

Contribution

It introduces the concept of a critical boson sphere (CBS) and analyzes its effects on fermion behavior, revealing a marginal NFL fixed point in a large boson flavor limit.

Findings

Identification of a marginal non-Fermi liquid fixed point.

Suppression of Landau damping due to infinite boson channels.

Emergence of epsilon poles in fermion self-energy and Yukawa vertex.

Abstract

We study the fermion-boson coupled system in $d=3-\epsilon$ space dimensions near the quantum phase transition; infinite many boson modes located on a sphere become critical simultaneously, which is dubbed "critical boson sphere" (CBS). The fermions on the Fermi surface can be scattered to nearby points located on a boson ring in the low-energy limit. The number of boson scattering channel $N_{B}$ is also infinite, which renders the well-known Landau damping effect largely suppressed. The one-loop renormalization group analysis is performed with asymptotic $\epsilon$-expansion. We find that the fermion self-energy and Yukawa interaction vertex are dressed with $\epsilon$ poles; in addition, there emerges an enhancement due to the curvature effect of CBS. In certain perturbative regimes, we identify a marginal non-Fermi liquid (NFL) fixed point that exists intrinsically in the large-$N_B$ limit. The infinite critical bosons comprise a physical realization of the flavor degrees of freedom which has been proposed for matrix large-$N_B$ bosons.