Temporal Entanglement, Quasiparticles, and the Role of Interactions

Area of Science:

• Quantum Many-Body Dynamics
• Integrable Systems
• Quantum Information

Background:

• The Feynman-Vernon influence matrix (IM) describes the effect of a quantum system on its local subsystems.
• For noninteracting quasiparticles, the temporal entanglement (TE) of the IM follows an area law, enabling efficient matrix-product state representations.
• The impact of integrable interactions on TE and the potential violation of the area law remain open questions.

Purpose of the Study:

• To investigate whether integrable interactions alter the temporal entanglement (TE) behavior in discrete quantum many-body dynamics.
• To determine if interactions lead to violations of the area law for the temporal entanglement of the influence matrix.

Main Methods:

• Analysis of quantum quenches in discrete integrable dynamics, specifically the real-time Trotterization of the interacting XXZ Heisenberg model.
• Exact analytical solution at the dual-unitary point.
• Numerical calculations for generic system parameters.

Main Results:

• Away from the noninteracting limit, the temporal entanglement (TE) exhibits logarithmic growth in time.
• This logarithmic growth signifies a violation of the area law for the temporal entanglement of the influence matrix.
• Integrable interactions play a nontrivial role in the dynamics of temporal entanglement.

Conclusions:

• Integrable interactions in quantum many-body systems lead to a violation of the area law for temporal entanglement.
• The findings challenge the efficiency of matrix-product state representations for simulating local dynamics in interacting integrable systems.
• Raises questions about the development of new simulation techniques for such systems.