Quantum complexity and localization in random and time-periodic unitary circuits
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915295300419584 |
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| author | Sahu, Himanshu Bhattacharya, Aranya Nath, Pingal Pratyush |
| author_facet | Sahu, Himanshu Bhattacharya, Aranya Nath, Pingal Pratyush |
| contents | We study the growth and saturation of Krylov spread (K-) complexity under random quantum circuits. In Haar-random unitary evolution, we show that, for large system sizes, K-complexity grows linearly before saturating at a late-time value of $D/2$, where $D$ is the Hilbert space dimension, at timescales $\sim D$. Our numerical analysis encompasses two classes of random circuits: brick-wall random unitary circuits and Floquet random circuits. In brick-wall case, K-complexity exhibits dynamics consistent with Haar-random unitary evolution, while the inclusion of measurements significantly slows its growth down. For Floquet random circuits, we show that localized phases lead to reduced late-time saturation values of K-complexity, forbye we utilize these saturation values to probe the transition between thermal and many-body localized phases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03656 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum complexity and localization in random and time-periodic unitary circuits Sahu, Himanshu Bhattacharya, Aranya Nath, Pingal Pratyush Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory We study the growth and saturation of Krylov spread (K-) complexity under random quantum circuits. In Haar-random unitary evolution, we show that, for large system sizes, K-complexity grows linearly before saturating at a late-time value of $D/2$, where $D$ is the Hilbert space dimension, at timescales $\sim D$. Our numerical analysis encompasses two classes of random circuits: brick-wall random unitary circuits and Floquet random circuits. In brick-wall case, K-complexity exhibits dynamics consistent with Haar-random unitary evolution, while the inclusion of measurements significantly slows its growth down. For Floquet random circuits, we show that localized phases lead to reduced late-time saturation values of K-complexity, forbye we utilize these saturation values to probe the transition between thermal and many-body localized phases. |
| title | Quantum complexity and localization in random and time-periodic unitary circuits |
| topic | Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2409.03656 |