Quench dynamics and scaling laws in topological nodal loop semimetals

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.

8 pages, 7 figures; references added

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• Scaling and Universality at Ramped Quench Dynamical Quantum Phase Transition
• Exploring Dynamical Phase Transitions in the XY Chain through Linear Quench: Early and Long-term Perspectives
• Interaction quench of dipolar bosons in a one-dimensional optical lattice
• Kibble-Zurek behavior in a topological phase transition with a quadratic band crossing
• Vortex loop dynamics and dynamical quantum phase transitions in 3D fermion matter
• Emerging topological characterization in non-equilibrium states of quenched Kitaev chains
• Dynamical characterization of $Z_2$ Floquet topological phases via quantum quenches
• Distinguishing dynamical quantum criticality through local fidelity distances
• Structure and scaling of Kitaev chain across a quantum critical point in real space
• Dynamical Phase Transitions in Periodically Driving 1D Ising Model
• Dynamical Geometry of the Haldane Model under a Quantum Quench
• Finite-rate quench in disordered Chern and $Z_2$ topological insulators