Exact fermionic Green's functions from holograpny

TL;DR

This paper constructs charged dilatonic black holes with zero entropy at zero temperature, allowing exact solutions for fermionic Green's functions, revealing Fermi surfaces and pole dynamics in holographic models.

Contribution

It provides exact analytical solutions for fermionic Green's functions in a new class of charged dilatonic black holes, enhancing the understanding of holographic fermionic systems.

Findings

Existence of Fermi surfaces in the holographic models.

Exact solutions for fermionic Green's functions in special functions.

Observation of pole motion in the complex frequency plane.

Abstract

We construct a series of charged dilatonic black holes which share zero entropy in the zero temperature limit using Einstein-Maxwell-Dilaton theories. In these black holes, the wave functions and the Green's functions of massless fermions can be solved exactly in terms of special functions in the phase space of $(\omega,k)$. We observe that for sufficiently large charge, there are many poles in the Green's function with vanishing $\omega$, which strongly signifies that Fermi surfaces exist in these holographic systems. The new distinguishing properties of the Green's function arising in these systems were illustrated with great details. We also study the poles motion of the Green's function for arbitrary (complex) frequency. Our analytic results provide a more realistic and elegant approach to study strongly correlated fermionic systems using gauge/gravity duality.