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

This study presents a detailed analysis of critical phenomena in a holographic Weyl semi-metal (WSM) using the $D3\mathrm{/}D7$ 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.