## SciPost Submission Page

# Operator Entanglement in Local Quantum Circuits I: Maximally Chaotic Dual-Unitary Circuits

### by Bruno Bertini, Pavel Kos, Tomaz Prosen

### Submission summary

As Contributors: | Bruno Bertini |

Arxiv Link: | https://arxiv.org/abs/1909.07407v1 |

Date submitted: | 2019-10-01 |

Submitted by: | Bertini, Bruno |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | Quantum Physics |

### Abstract

The entanglement in operator space is a well established measure for the complexity of the quantum many-body dynamics. In particular, that of local operators has recently been proposed as dynamical chaos indicator, i.e. as a quantity able to discriminate between quantum systems with integrable and chaotic dynamics. For chaotic systems the local-operator entanglement is expected to grow linearly in time, while it is expected to grow at most logarithmically in the integrable case. Here we study local-operator entanglement in dual-unitary quantum circuits, a class of "statistically solvable" quantum circuits that we recently introduced. We show that for "maximally-chaotic" dual-unitary circuits the local-operator entanglement grows linearly and we provide a conjecture for its asymptotic behaviour which is in excellent agreement with the numerical results. Interestingly, our conjecture also predicts a "phase transition" in the slope of the local-operator entanglement when varying the parameters of the circuits.