Holographic Lifshitz fermions and exponentially suppressed spectral weight

TL;DR

This paper investigates how Lifshitz scale invariance leads to exponential suppression of spectral weight at low frequencies in holographic models, revealing a universal tunneling barrier effect for fermions and scalars.

Contribution

It demonstrates that the exponential suppression in spectral weight is universal for Lifshitz holography and extends the understanding from scalar to fermionic cases.

Findings

Spectral weight is exponentially suppressed at low frequencies.

The suppression factor is universal and depends only on frequency ratio and critical exponent.

The tunneling barrier form is identical for scalar and fermionic holographic Green's functions.

Abstract

The absence of fixed momentum excitations in a theory with Lifshitz scale invariance gives rise to exponential suppression of spectral weight in the low-frequency limit. In the holographic dual, this suppression arises as a consequence of a tunneling barrier that decouples the horizon from the boundary. We compute the spin-1/2 holographic Green's function and show that the form of the barrier is identical to that of the scalar case. We furthermore demonstrate that the suppression factor is universal in the $\hat\omega\to0$ limit where $\hat\omega=\omega/|\vec k|^z$. In particular, it depends only on $\hat\omega$ and the critical exponent $z$, and is independent of scaling dimension and spin.