Fermi Liquid Fixed Point Deformations due to Codimension Two Defects

TL;DR

This paper investigates how codimension-two defects in Fermi liquids induce a marginally relevant deformation in the renormalization group flow, driven by spatial anisotropy and defect geometry, affecting low-energy properties.

Contribution

It introduces a novel mechanism for RG flow deformation caused by codimension-two defects, distinct from the Kondo problem, emphasizing geometric and anisotropic effects.

Findings

RG flow scales with defect length

Hole fluctuations are suppressed along the defect direction

Dislon modes become relevant above a certain frequency

Abstract

We show that codimension-two defects in Fermi liquids deform the renormalization group flow via a marginally relevant coupling. The mechanism for generating the flow is distinct from the case of the Kondo problem (codimension-three defects) in that the effective particle-hole asymmetry that leads to the log running is due to the spatial anisotropy generated by the defect. The mechanism for the log generation has a simple geometric explanation which shows that hole fluctuations are suppressed as the incoming momentum is taken to be along the direction of the defect. The RG flow time is shown to scale with the length of the defect. We also show that the dislon, the Goldstone mode localized to the defect, couples in a non-derivative fashion to the bulk fermions and becomes relevant above the dislons' Debye frequency which depends upon the defect tension.