Non-Fermi Liquid Behavior in 3+1 Dimensions with PT Invariant Gauge Field: An Renormalization Group Approach

TL;DR

This paper investigates non-Fermi liquid behavior in 3+1 dimensions through a renormalization group analysis of a coupled Fermi surface and gauge field, revealing a non-trivial fixed point and breakdown of Landau Fermi liquid theory.

Contribution

It introduces a calibrated scaling approach for RG analysis in 3+1 dimensions and demonstrates the existence of a non-trivial fixed point affecting fermion behavior.

Findings

Presence of a non-trivial fixed point controlling gauge interactions

Two-point Green's function shows non-quasi particle poles

Fermion anomalous dimension is gauge dependent but persists under gauge renormalization

Abstract

We introduce a Hamiltonian coupled between a normal Fermi surface and a polarized Maxwell type gauge field.We adopt a {\it calibrated scaling } approach in order to be consistent with the results obtained at $2+1$ dimensions as well as the Weinberg's theo rem. Renormalization group equations are calculated by using a dimension regulator. It turns out that the gauge interaction is controlled by a non-trivial fixed point. The two-point Green's function can thus be calculated accurately in the low temperature limit and possesses a non-quasi particle pole which signals the break down of the Landau Fermi liquid theory. In addition,we show that the anomalous dimension of fermion field is in general gauge dependent. But it will survive under generic gauge choice due to the renormalization of the gauge fixing parameter.