Holographic fermions in asymptotically scaling geometries with hyperscaling violation

TL;DR

This paper explores holographic fermions in geometries with hyperscaling violation, demonstrating Green function sum rules, analyzing dispersion relations, and revealing how charge and hyperscaling affect Fermi surface structures.

Contribution

It generalizes fermion behavior in Lifshitz spacetime to include hyperscaling violation, showing decoupling of fermion mass from unitarity bounds and detailed Fermi surface evolution.

Findings

Green functions satisfy ARPES sum rules with a UV brane source.

Fermi surface structures evolve with charge, forming shells and wide bands.

Spectral features are smoothed out as hyperscaling violation increases.

Abstract

We investigate holographic fermions in general asymptotically scaling geometries with hyperscaling violation exponent $\theta$, which is a natural generalization of fermions in Lifshitz spacetime. We prove that the retarded Green functions in this background satisfy the ARPES (angle-resolved photoemission spectroscopy) sum rules by introducing a dynamical source on a UV brane for zero density fermionic systems. The big difference from the Lifshitz case is that the mass of probe fermions decoupled from the UV theory and thus has no longer been restricted by unitarity bound. We also study finite density fermions at finite temperature, with dynamical exponent $z=2$. We find that the dispersion relation is linear but the logarithm of the spectral function is not linearly related to the logarithm of $k_\bot =k-k_F$, independent of charge $q$ and $\theta$. Furthermore, we show that with the increasing of charge, new branches of Fermi surfaces emerge and tend to gathering together to form a shell-like structure when the charge reaches some critical value beyond which a wide band pattern appears in the momentum-charge plane. However, all sharp peaks will be smoothed out when $\theta$ increases, no matter how much large the charge is.