Charged Lifshitz black hole and probed Lorentz-violation fermions from holography

TL;DR

This paper constructs a charged Lifshitz black hole in Horava-Lifshitz gravity and explores how Lorentz-violation in fermions affects their spectral properties, revealing a phase transition from non-Fermi liquid to Fermi liquid behavior.

Contribution

It introduces a new charged Lifshitz black hole solution with Lorentz-violation fermions and studies their spectral behavior holographically, highlighting a phase transition.

Findings

Lorentz-violation enhances spectral peak and Fermi momentum.

A critical Lorentz-violation value induces a transition from non-Fermi liquid to Fermi liquid.

The black hole exhibits Lifshitz scaling in UV and Lorentz invariance in IR.

Abstract

We analytically obtain a new charged Lifshtitz solution by adding a non-relativistic Maxwell field in Horava-Lifshitz gravity. The black hole exhibits an anisotropic scaling between space and time (Lifshitz scaling) in the UV limit, while in the IR limit, the Lorentz invariance is recovered. We introduce the probed Lorentz-violation fermions into the background and holographically investigate the spectral properties of the dual fermionic operator. The Lorentz-violation of fermions will enhance the peak and corresponds larger fermi momentum, which compensates the non-relativistic bulk effect of the dynamical exponent. For a fixed $z$, when the Lorentz-violation of fermions increases to a critical value, the behavior of the low energy excitation goes from a non-Fermi liquid type to a fermi liquid type, which implies a kind of phase transition.