Temporal Entanglement Transitions in the Periodically Driven Ising Chain

Abstract: Periodically driven quantum systems can host non-equilibrium phenomena without static analogs, including in their entanglement dynamics. Here, we discover $temporal$ $entanglement$ $transitions$ in a Floquet spin chain, which correspond to a quantum phase transition in the spectrum of the entanglement Hamiltonian and are signaled by dynamical spontaneous symmetry breaking. We show that these transitions are entanglement-driven, i.e., they require initially entangled states and remain invisible to conventional local observables. Intriguingly, we find these transitions across a broad range of driving frequencies (from adiabatic to high-frequency regime) and independently of drive details, where they manifest as periodic, sharp entanglement spectrum reorganizations marked by the Schmidt-gap closure, a vanishing entanglement echo, and symmetry-quantum-number flips. At high frequencies, the entanglement Hamiltonian acquires an intrinsic timescale decoupled from the drive period, rendering the transitions genuine steady-state features. Finite-size scaling reveals universal critical behavior with correlation-length exponent $\nu=1$, matching equilibrium Ising universality despite its emergence from purely dynamical mechanisms decoupled from static criticality. Our work establishes temporal entanglement transitions as novel features in Floquet quantum matter.