The Pauli exclusion principle at strong coupling: Holographic matter and momentum space
Richard J. Anantua, Sean A. Hartnoll, Victoria L. Martin, David M. Ramirez
TL;DR
We address whether strong-coupling holographic matter preserves a momentum-space structure reminiscent of Pauli exclusion by examining low-energy current spectral densities at finite density in two holographic models. The analysis considers semi-local quantum liquids with $z\to\infty$ (parameterized by $\eta=-\theta/z$) and a D3/D5 probe-brane system, focusing on transverse and longitudinal channels. In the semi-local case, transverse spectral weight exhibits a sharp boundary at a finite momentum $k_\star$ with divergent response for $k<k_\star$ and vanishing weight for $k>k_\star$, while the longitudinal weight is IR-irrelevant; the special case $\eta=1$ yields enhanced symmetry and linear-in-$T$ resistivity with impurities. In the D3/D5 system, the transverse spectral weight is analytic with a finite support up to $k_\star=Q/(2\mu_0)$ and exponential suppression beyond, while the longitudinal sector is numerically characterized and shows reduced weight and a zero-sound feature at small momentum, collectively illustrating how strong coupling reorganizes momentum space in novel quantum liquids.
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.