Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908293265358848 |
|---|---|
| author | Song, Menghan Zeng, Zhaoyi Wang, Ting-Tung You, Yi-Zhuang Meng, Zi Yang Zhang, Pengfei |
| author_facet | Song, Menghan Zeng, Zhaoyi Wang, Ting-Tung You, Yi-Zhuang Meng, Zi Yang Zhang, Pengfei |
| contents | We investigate operator dynamics and entanglement growth in dual-unitary circuits, a class of locally scrambled quantum systems that enables efficient simulation beyond the exponential complexity of the Hilbert space. By mapping the operator evolution to a classical Markov process,we perform Monte Carlo simulations to access the time evolution of local operator density and entanglement with polynomial computational cost. Our results reveal that the operator density converges exponentially to a steady-state value, with analytical bounds that match our simulations. Additionally, we observe a volume-law scaling of operator entanglement across different subregions,and identify a critical transition from maximal to sub-maximal entanglement growth, governed by the circuit's gate parameter. This transition, confirmed by both mean-field theory and Monte Carlo simulations, provides new insights into operator entanglement dynamics in quantum many-body systems. Our work offers a scalable computational framework for studying long-time operator evolution and entanglement, paving the way for deeper exploration of quantum information dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00953 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits Song, Menghan Zeng, Zhaoyi Wang, Ting-Tung You, Yi-Zhuang Meng, Zi Yang Zhang, Pengfei Quantum Physics Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory We investigate operator dynamics and entanglement growth in dual-unitary circuits, a class of locally scrambled quantum systems that enables efficient simulation beyond the exponential complexity of the Hilbert space. By mapping the operator evolution to a classical Markov process,we perform Monte Carlo simulations to access the time evolution of local operator density and entanglement with polynomial computational cost. Our results reveal that the operator density converges exponentially to a steady-state value, with analytical bounds that match our simulations. Additionally, we observe a volume-law scaling of operator entanglement across different subregions,and identify a critical transition from maximal to sub-maximal entanglement growth, governed by the circuit's gate parameter. This transition, confirmed by both mean-field theory and Monte Carlo simulations, provides new insights into operator entanglement dynamics in quantum many-body systems. Our work offers a scalable computational framework for studying long-time operator evolution and entanglement, paving the way for deeper exploration of quantum information dynamics. |
| title | Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.00953 |