Temporal Entanglement Transitions in the Periodically Driven Ising Chain.

Area of Science:

• Quantum physics
• Condensed matter physics
• Quantum information science

Background:

• Periodically driven quantum systems exhibit unique nonequilibrium phenomena.
• Entanglement dynamics in these systems can display complex behaviors without static counterparts.

Purpose of the Study:

• To discover and characterize novel transitions in the entanglement dynamics of Floquet spin chains.
• To identify the underlying symmetry principles governing these transitions.
• To investigate the universality and characteristics of these transitions across different driving regimes.

Main Methods:

• Analysis of entanglement Hamiltonian spectrum in a driven Floquet spin chain.
• Identification of symmetry principles including global symmetry preservation (Z_{2}) and subsystem-parity sector weights.
• Investigation of dynamical spontaneous symmetry breaking as a signal for transitions.
• Finite-size scaling analysis to determine critical behavior and universality.

Main Results:

• Discovery of temporal entanglement transitions (TETs) in Floquet spin chains.
• TETs correspond to quantum phase transitions in the entanglement Hamiltonian spectrum.
• Transitions are signaled by dynamical spontaneous symmetry breaking and are governed by specific symmetry conditions.
• Manifestations include entanglement spectrum reorganizations, Schmidt-gap closure, vanishing entanglement echo, and symmetry-quantum-number flips.
• Universal critical behavior with correlation-length exponent ν=1 observed, matching equilibrium Ising universality.
• Transitions are robust across various driving frequencies and drive details, and are decoupled from local observables.

Conclusions:

• Temporal entanglement transitions are novel, robust features in Floquet quantum matter.
• These transitions offer a new perspective on quantum phase transitions in driven systems.
• The universality of TETs, despite their dynamical origin, highlights deep connections between driven and equilibrium critical phenomena.