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A Framework for Studying a Quantum Critical Metal in the Limit $N_f\rightarrow0$
by Petter Säterskog
This is not the current version.
|As Contributors:||Petter Säterskog|
|Arxiv Link:||https://arxiv.org/abs/1711.04338v1 (pdf)|
|Date submitted:||2017-11-21 01:00|
|Submitted by:||Säterskog, Petter|
|Submitted to:||SciPost Physics|
We study a model in 1+2 dimensions composed of a spherical Fermi surface of $N_f$ flavors of fermions coupled to a massless scalar. We present a framework to non-perturbatively calculate general fermion $n$-point functions of this theory in the limit $N_f\rightarrow0$ followed by $k_F\rightarrow\infty$ where $k_F$ sets both the size and curvature of the Fermi surface. Using this framework we calculate the zero-temperature fermion density-density correlation function in real space and find an exponential decay of Friedel oscillations.
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Reports on this Submission
Anonymous Report 1 on 2017-12-20 Invited Report
- Cite as: Anonymous, Report on arXiv:1711.04338v1, delivered 2017-12-20, doi: 10.21468/SciPost.Report.303
1. Treatment of the problem is technically sound.
2. Demonstration of a non-perturbative effect of the fermion-boson interaction in the density-density response.
3. The introduction contains a good exposition of the problem.
1. The conclusion foregoes a discussion of the principal result with respect to the physical properties of the system at hand.
The author studies the correlation functions of a two-dimensional metal which is strongly coupled to gapless bosons. Building on earlier related work, the present publication elaborates on the density-density response in a strictly controllable, albeit somehow arbitrary limit which is non-perturbative in the coupling strength. As the main result, the density-density correlation features an exponentially fast extinction in real space, which appears only beyond perturbation theory.
I can recommend the publication, but I suggest to elaborate in better detail on the significance of the result for critical metals in two dimensions.
The author might consider to widen the scope of the discussion to include some implications of their fast decay. What does this mean for the stability of the critical theory at Q=0, and for the stability of approximations where the Landau damping is incorporated from the outset? Can the improved density-density correlator be used to supplement previous N_f->0 methods?