Critical Entanglement Dynamics at Dynamical Quantum Phase Transitions

We investigate the critical behavior of momentum-space entanglement entropy at dynamical quantum phase transitions (DQPTs) in translationally invariant two-band insulators and superconductors. By analyzing the Su-Schrieffer-Heeger model, the quantum XY chain, and the Haldane model, we establish that the geometric DQPT condition $\hat{\textbf{d}}_{\textbf{k}}^{i} \cdot \hat{\textbf{d}}_{\textbf{k}}^{f} = 0$ manifests as exact degeneracy $p_{\textbf{k}^{*}}=1/2$ in the entanglement spectrum defined with respect to the post-quench eigenbasis, yielding a maximal momentum-space entropy of $\ln 2$. In one dimension, critical momenta appear as isolated points, whereas in two dimensions they form continuous one-dimensional manifolds, reflecting the dimensional dependence of the underlying critical structure. Importantly, alternative bipartitions such as the sublattice basis produce qualitatively different behavior: the entropy becomes explicitly time-dependent and attains a minimum at DQPT critical times, underscoring the essential role of basis selection. Our results establish that momentum-space entanglement entropy, when evaluated in the appropriate eigenbasis, provides a robust, time-independent diagnostic of DQPTs and offers a unified geometric perspective linking entanglement, topology, and non-equilibrium criticality.