Spectral function of a localized fermion coupled to the Wilson-Fisher conformal field theory

TL;DR

This paper investigates the spectral properties of a localized fermion interacting with a 2+1D conformal field theory near quantum critical points, providing insights into fermionic dynamics in quantum phase transitions.

Contribution

It introduces a novel analysis of a fermion coupled to a 2+1D CFT, utilizing a defect line mapping to explore spectral functions near quantum criticality.

Findings

Fermionic spectral functions relevant to 2D metals near quantum critical points.

Mapping to a defect line CFT offers a new analytical approach.

Results applicable to intermediate temperature regimes where Landau damping is negligible.

Abstract

We describe the dynamics of a single fermion in a dispersionless band coupled to the 2+1 dimensional conformal field theory (CFT) describing the quantum phase transition of a bosonic order parameter with N components. The fermionic spectral functions are expected to apply to the vicinity of quantum critical points in two-dimensional metals over an intermediate temperature regime where the Landau damping of the order parameter can be neglected. Some of our results are obtained by a mapping to an auxiliary problem of a CFT containing a defect line with an external field which locally breaks the global O(N) symmetry.