Free Independence and the Noncrossing Partition Lattice in Dual-Unitary Quantum Circuits
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866918096647749632 |
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| author | Chen, Hyaline Junhe Kudler-Flam, Jonah |
| author_facet | Chen, Hyaline Junhe Kudler-Flam, Jonah |
| contents | We investigate details of the chaotic dynamics of dual-unitary quantum circuits by evaluating all $2k$-point out-of-time-ordered correlators. For the generic class of circuits, by writing the correlators as contractions of a class of quantum channels, we prove their exponential decay. This implies that local operators separated in time approach free independence. Along the way, we develop a replica trick for dual-unitary circuits, which may be useful and of interest in its own right. We classify the relevant eigenstates of the replica transfer matrix by paths in the lattice of noncrossing partitions, combinatorial objects central to free probability theory. Interestingly, the noncrossing lattice emerges even for systems without randomness and with small onsite Hilbert space dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17226 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Free Independence and the Noncrossing Partition Lattice in Dual-Unitary Quantum Circuits Chen, Hyaline Junhe Kudler-Flam, Jonah Statistical Mechanics High Energy Physics - Theory Mathematical Physics Quantum Physics We investigate details of the chaotic dynamics of dual-unitary quantum circuits by evaluating all $2k$-point out-of-time-ordered correlators. For the generic class of circuits, by writing the correlators as contractions of a class of quantum channels, we prove their exponential decay. This implies that local operators separated in time approach free independence. Along the way, we develop a replica trick for dual-unitary circuits, which may be useful and of interest in its own right. We classify the relevant eigenstates of the replica transfer matrix by paths in the lattice of noncrossing partitions, combinatorial objects central to free probability theory. Interestingly, the noncrossing lattice emerges even for systems without randomness and with small onsite Hilbert space dimension. |
| title | Free Independence and the Noncrossing Partition Lattice in Dual-Unitary Quantum Circuits |
| topic | Statistical Mechanics High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2409.17226 |