The Pauli exclusion principle at strong coupling: Holographic matter and momentum space

TL;DR

This paper explores how the Pauli exclusion principle manifests in strongly interacting quantum matter with holographic duals, revealing momentum space features akin to Fermi surfaces and analyzing their temperature and impurity effects.

Contribution

It provides the first detailed holographic analysis of momentum space spectral weight and Fermi surface-like features in strongly coupled systems with semi-local quantum criticality and probe brane models.

Findings

Sharp spectral weight discontinuity at nonzero momentum for 0<eta<2

Linear temperature dependence of resistivity at eta=1

Analytic spectral weight expression for D3/D5 system

Abstract

For free fermions at finite density, the Pauli exclusion principle is responsible for the existence of a Fermi surface and the consequent presence of low energy spectral weight over a finite range of momenta. We investigate the extent to which this effect occurs in strongly interacting quantum matter with a holographic dual. We obtain the low energy current-current spectral weight in two holographic frameworks at finite density: systems exhibiting semi-local quantum criticality (with a low temperature entropy density vanishing like s ~ T^eta), and a probe D3/D5 system. For the semi-local theory with 0 < eta < 2 we find a sharp discontinuity in the transverse spectral weight at a nonzero momentum k_*. The case eta = 1 is found to have additional symmetries and is soluble even at nonzero temperature. We show that this case exhibits a robust linear in temperature resistivity in the presence of random charged impurities. For the probe D3/D5 system we find an analytic expression for the low energy spectral weight as a function of momentum. The spectral weight is supported below a specific momentum k_* and is exponentially suppressed at higher momenta.