Abstract
We study a model in 2+1 dimensions composed of a Fermi surface of N_fNf flavors of fermions coupled to scalar fluctuations near quantum critical points (QCPs). The N_f\rightarrow0Nf→0 limit allows us to non-perturbatively calculate the long-range behavior of fermion correlation functions. We use this to calculate charge, spin and pair susceptibilities near different QCPs at zero and finite temperatures, with zero and finite order parameter gaps. While fluctuations smear out the fermionic quasiparticles, we find QCPs where the overall effect of fluctuations leads to enhanced pairing. We also find QCPs where the fluctuations induce spin and charge density wave instabilities for a finite interval of order parameter fluctuation gaps at T=0T=0. We restore a subset of the diagrams suppressed in the N_f\rightarrow0Nf→0 limit, all diagrams with internal fermion loops with at most 2 vertices, and find that this does not change the long-range behavior of correlators except right at the QCPs.
Highlights
We start each subsection with a brief description of the quantum phase transition and how its fluctuations couple to the fermions, i.e. what the structure of λσ(θ ) is. We consider another system that can be described by the same model, fermions coupled to an emergent gauge field
We consider an l = 2 charge nematic quantum critical point such as the ones that have been observed in the Cu- [1,2] and Fe- [3,4,5] based SCs
These quantum critical points (QCPs) are due to electronic instabilities towards a state where the Fermi surface shape breaks the C4 rotational symmetry of the lattice
Summary
Interacting fermions at finite density form a rich physical system that can be used to describe many condensed matter phenomena. It was possible to obtain an (almost) closed form expression, and it showed that the fermion dispersion becomes non-monotonic due to corrections from the critical fluctuations This was extended in [27] where a framework was developed to calculate general fermion n-point correlation functions in the small Nf limit of a fermion-boson model. There are earlier works in the small Nf limit where the authors incorporated these effects from the start by using an explicitly Landau-damped boson when calculating the real space fermion two-point function [8, 28,29,30,31]. In this paper we explore how critical fluctuations can lead to instabilities of finite density fermions in the small Nf limit We do this by using the framework developed in [27] to calculate spin, charge and pair correlation functions. We have reintroduced the a indices and the h±a (τ, x) are defined with the propagator Da(ωn, kx , ky ) for the field φa
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