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

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|November 4, 2022
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Summary
This summary is machine-generated.

Operator entanglement (OE) typically decreases in dissipative systems. However, this study reveals that dephasing causes OE to unexpectedly rise logarithmically over time in 1D many-body models.

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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.