Holographic fermions at strong translational symmetry breaking: a Bianchi-VII case study

TL;DR

This paper investigates how strong translational symmetry breaking affects the fermion spectral function in holographic strange metals, revealing that quasi-particles gain finite lifetime and disappear at certain transition points.

Contribution

It demonstrates how to compute the fermion spectral function in Bianchi-VII geometries for arbitrary symmetry breaking strength, highlighting the behavior of quasi-particles and spectral transitions.

Findings

Small changes in fermion response deep in the strange metal regime.

Quasi-particles acquire finite lifetime at finite symmetry breaking.

Complete disappearance of quasi-particles at the IR transition.

Abstract

It is presently unknown how strong lattice potentials influence the fermion spectral function of the holographic strange metals predicted by the AdS/CFT correspondence. This embodies a crucial test for the application of holography to condensed matter experiments. We show that for one particular momentum direction this spectrum can be computed for arbitrary strength of the effective translational symmetry breaking potential of the so-called Bianchi-VII geometry employing ordinary differential equations. Deep in the strange metal regime we find rather small changes to the single-fermion response computed by the emergent quantum critical IR, even when the potential becomes relevant in the infra-red. However, in the regime where holographic quasi-particles occur, defining a Fermi surface in the continuum, they acquire a finite lifetime at any finite potential strength. At the transition from irrelevancy to relevancy of the Bianchi potential in the deep infra-red the quasi-particle remnants disappear completely and the fermion spectrum exhibits a purely relaxational behaviour.