Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits
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 an...
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| Format: | Article |
| Language: | English |
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SciPost
2020-04-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.8.4.067 |
| _version_ | 1818287798635986944 |
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| author | Bruno Bertini, Pavel Kos, Tomaz Prosen |
| author_facet | Bruno Bertini, Pavel Kos, Tomaz Prosen |
| author_sort | Bruno Bertini, Pavel Kos, Tomaz Prosen |
| collection | DOAJ |
| description | 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 identify a class of
"completely chaotic" dual-unitary circuits where 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. |
| first_indexed | 2024-12-13T01:46:13Z |
| format | Article |
| id | doaj.art-43e090d5cb094981932df6e0a2a4d8fa |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-12-13T01:46:13Z |
| publishDate | 2020-04-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-43e090d5cb094981932df6e0a2a4d8fa2022-12-22T00:03:38ZengSciPostSciPost Physics2542-46532020-04-018406710.21468/SciPostPhys.8.4.067Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary CircuitsBruno Bertini, Pavel Kos, Tomaz ProsenThe 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 identify a class of "completely chaotic" dual-unitary circuits where 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.https://scipost.org/SciPostPhys.8.4.067 |
| spellingShingle | Bruno Bertini, Pavel Kos, Tomaz Prosen Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits SciPost Physics |
| title | Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits |
| title_full | Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits |
| title_fullStr | Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits |
| title_full_unstemmed | Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits |
| title_short | Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits |
| title_sort | operator entanglement in local quantum circuits i chaotic dual unitary circuits |
| url | https://scipost.org/SciPostPhys.8.4.067 |
| work_keys_str_mv | AT brunobertinipavelkostomazprosen operatorentanglementinlocalquantumcircuitsichaoticdualunitarycircuits |