Rise and Fall, and Slow Rise Again, of Operator Entanglement under Dephasing

Area of Science:

• Quantum Information Theory
• Condensed Matter Physics
• Statistical Mechanics

Background:

• Operator entanglement (OE) quantifies quantum operator complexity and approximability by matrix product operators (MPOs).
• Dissipative evolution in 1D many-body systems is expected to lead to simple stationary states with suppressed OE after initial growth.

Purpose of the Study:

• Investigate the behavior of OE in 1D many-body models under dissipative evolution, specifically focusing on dephasing.
• Determine if the expected suppression of OE by dissipation holds true for dephasing dynamics.

Main Methods:

• Simulations using matrix product operators (MPOs) for infinite-length chains.
• Analytical arguments for regimes of strong dephasing.

Main Results:

• Contrary to expectations, dephasing does not suppress OE; instead, it causes a logarithmic increase at long times after an initial rise and fall.
• This logarithmic growth is linked to a U(1) conservation law.
• Universal growth rates of 1/4log₂(t) for XXZ and Bose-Hubbard models, and 1/2log₂(t) for the Fermi-Hubbard model were identified.
• The phenomenon is traced back to anomalous classical diffusion processes.

Conclusions:

• Dephasing introduces a novel, non-monotonic behavior in operator entanglement, challenging previous assumptions about dissipative quantum systems.
• The observed logarithmic growth highlights the importance of conservation laws in shaping operator complexity under dissipation.
• This work provides new insights into the dynamics of quantum information and complexity in open quantum systems.