Temporal Entanglement Transitions in the Periodically Driven Ising Chain

Periodically driven quantum systems can host nonequilibrium phenomena without static analogs, including in their entanglement dynamics. Here, we discover temporal entanglement transitions (TETs) 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 identify the symmetry principles underlying these transitions: they appear when the driven Hamiltonian preserves global symmetry (here, Z₂), the initial state respects this symmetry, and the reduced density matrix carries weight in both subsystem-parity sectors, with TETs occurring precisely when the sector weights become equal (given the previous two conditions are also satisfied). Intriguingly, we find these transitions across a broad range of driving frequencies (from adiabatic to high-frequency regime) and independent 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, while remaining invisible to conventional local observables. 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 ν=1, matching equilibrium Ising universality despite its emergence from purely dynamical mechanisms decoupled from static criticality. Our Letter establishes TETs as novel features in Floquet quantum matter.