Non-Linear Dynamics and Critical Phenomena in the Holographic Landscape of Weyl Semimetals

TL;DR

This paper investigates critical phenomena and phase transitions in holographic Weyl semimetals, revealing quantum and thermal phase transitions driven by electric fields and background parameters, with numerical critical exponents akin to mean-field theory.

Contribution

It provides a novel holographic analysis of non-linear responses and phase transitions in Weyl semimetals, including quantum and thermal critical behaviors, using the D3/D7 brane model.

Findings

Identification of a quantum phase transition at zero temperature with a reconnection phenomenon.

Demonstration of first- and second-order phase transitions at finite temperature.

Numerical critical exponents consistent with mean-field theory.

Abstract

This study presents a detailed analysis of critical phenomena in a holographic Weyl semi-metal (WSM) using the $D3/D7$ brane configuration. The research explores the non-linear response of the longitudinal current \( J \) when subjected to an external electric field \( E \) at both zero and finite temperatures. At zero temperature, the study identifies a potential quantum phase transition in the \( J \)-\( E \) relationship, driven by background parameters the particle mass, and axial gauge potential. This transition is characterized by a unique reconnection phenomenon resulting from the interplay between WSM-like and conventional nonlinear conducting behaviors, indicating a quantum phase transition. Additionally, at non-zero temperature with dissipation, the system demonstrates first- and second-order phase transitions as the electric field and axial gauge potential are varied. The longitudinal conductivity is used as an order parameter to identify the current-driven phase transition. Numerical analysis reveals critical exponents in this non-equilibrium phase transition that show similarities to mean-field values observed in metallic systems.