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

This paper analyzes critical exponents in a holographic Weyl semi-metal (WSM) using the D3/D7 brane setup. We study the non-linear behavior of the longitudinal current J interacting with an external electric field E at zero and finite temperatures. At zero temperature, we identify a potential quantum phase transition in the J-E relationship driven by critical background parameters. At zero temperature, we pinpoint a potential quantum phase transition in the J-E relationship, driven by a critical ratio of background parameters. This transition is a unique reconnection phenomenon, emerging from the interplay between WSM-like and ordinary nonlinear conducting behaviors, signaling a quantum phase transition. At nonzero temperature, with dissipation, the system exhibits both first- and second-order phase transitions by varying the electric field and the axial anomaly. We introduce longitudinal conductivity as an order parameter for the current-driven phase transition. Remarkably, our numerical analysis indicates critical exponents in this non-equilibrium phase transition that resemble the mean-field values found in metallic systems. This study sheds light on critical phenomena in non-equilibrium states, offering new insights into the quantum critical behavior of holographic systems and the nonlinear dynamics in WSMs, with broader implications for quantum phase transitions in condensed matter physics and topological materials.