Dynamic Properties of Two-Dimensional Latticed Holographic System

TL;DR

This paper investigates how anisotropy affects the phase structure and dynamical properties of a two-dimensional holographic lattice system, revealing that small anisotropic deviations can significantly alter IR fixed points and phase behavior.

Contribution

It introduces the study of anisotropic effects on dynamical quantities and phase structure in a two-lattice holographic system, highlighting the impact of anisotropy on IR fixed points and quantum phase transitions.

Findings

Anisotropy influences the phase structure significantly.

IR fixed points can be non-AdS$_2 imes \\mathbb R^2$ in metallic phases.

Butterfly velocity and charge diffusion diagnose quantum phase transitions.

Abstract

We study the anisotropic properties of dynamical quantities: direct current (DC) conductivity, butterfly velocity, and charge diffusion. The anisotropy plays a crucial role in determining the phase structure of the two-lattice system. Even a small deviation from isotropy can lead to distinct phase structures, as well as the IR fixed points of our holographic systems. In particular, for anisotropic cases, the most important property is that the IR fixed point can be non-AdS$_2 \times \mathbb R^2$ even for metallic phases. As that of a one-lattice system, the butterfly velocity and the charge diffusion can also diagnose the quantum phase transition (QPT) in this two-dimensional anisotropic latticed system.