Quench dynamics and scaling laws in topological nodal loop semimetals

TL;DR

This paper investigates how quench dynamics reveal different universality classes in topological nodal loop semimetals, highlighting unique scaling laws, defect behaviors, and trajectory differences compared to Dirac-like systems.

Contribution

It introduces a comprehensive analysis of quench dynamics in nodal loop semimetals, uncovering novel scaling laws and defect behaviors not observed in traditional Dirac systems.

Findings

Reduced Kibble-Zurek scaling exponent with nodal loops

Path-dependent crossover in critical exponents at multicritical points

Mismatch between defect generation modes and quantum phase transitions

Abstract

We employ quench dynamics as an effective tool to probe different universality classes of topological phase transitions. Specifically, we study a model encompassing both Dirac-like and nodal loop criticalities. Examining the Kibble-Zurek scaling of topological defect density, we discover that the scaling exponent is reduced in the presence of extended nodal loop gap closures. For a quench through a multicritical point, we also unveil a path-dependent crossover between two sets of critical exponents. Bloch state tomography finally reveals additional differences in the defect trajectories for sudden quenches. While the Dirac transition permits a static trajectory under specific initial conditions, we find that the underlying nodal loop leads to complex time-dependent trajectories in general. In the presence of a nodal loop, we find, generically, a mismatch between the momentum modes where topological defects are generated and where dynamical quantum phase transitions occur. We also find notable exceptions where this correspondence breaks down completely.