Power-law entanglement growth from typical product states
Generic quantum many-body systems typically show a linear growth of the entanglement entropy after a quench from a product state. While entanglement is a property of the wave function, it is generated by the unitary time-evolution operator and is therefore reflected in its increasing complexity as q...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2019-11-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.1.033067 |
| _version_ | 1797211709912383488 |
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| author | Talía L. M. Lezama David J. Luitz |
| author_facet | Talía L. M. Lezama David J. Luitz |
| author_sort | Talía L. M. Lezama |
| collection | DOAJ |
| description | Generic quantum many-body systems typically show a linear growth of the entanglement entropy after a quench from a product state. While entanglement is a property of the wave function, it is generated by the unitary time-evolution operator and is therefore reflected in its increasing complexity as quantified by the operator entanglement entropy. Using numerical simulations of a static and a periodically driven quantum spin chain, we show that there is a robust correspondence between the entanglement entropy growth of typical product states and the operator entanglement entropy of the unitary evolution operator, while special product states, e.g., σ_{z} basis states, can exhibit faster entanglement production. In the presence of a disordered magnetic field in our spin chains, we show that both the wave function and operator entanglement entropies exhibit a power-law growth with the same disorder-dependent exponent and clarify the apparent discrepancy in previous results. These systems, in the absence of conserved densities, provide further evidence for slow information spreading on the ergodic side of the many-body localization transition. |
| first_indexed | 2024-04-24T10:30:48Z |
| format | Article |
| id | doaj.art-f8e9de41b0a74a93b99e4e6aeacb88b2 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:30:48Z |
| publishDate | 2019-11-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-f8e9de41b0a74a93b99e4e6aeacb88b22024-04-12T16:46:33ZengAmerican Physical SocietyPhysical Review Research2643-15642019-11-011303306710.1103/PhysRevResearch.1.033067Power-law entanglement growth from typical product statesTalía L. M. LezamaDavid J. LuitzGeneric quantum many-body systems typically show a linear growth of the entanglement entropy after a quench from a product state. While entanglement is a property of the wave function, it is generated by the unitary time-evolution operator and is therefore reflected in its increasing complexity as quantified by the operator entanglement entropy. Using numerical simulations of a static and a periodically driven quantum spin chain, we show that there is a robust correspondence between the entanglement entropy growth of typical product states and the operator entanglement entropy of the unitary evolution operator, while special product states, e.g., σ_{z} basis states, can exhibit faster entanglement production. In the presence of a disordered magnetic field in our spin chains, we show that both the wave function and operator entanglement entropies exhibit a power-law growth with the same disorder-dependent exponent and clarify the apparent discrepancy in previous results. These systems, in the absence of conserved densities, provide further evidence for slow information spreading on the ergodic side of the many-body localization transition.http://doi.org/10.1103/PhysRevResearch.1.033067 |
| spellingShingle | Talía L. M. Lezama David J. Luitz Power-law entanglement growth from typical product states Physical Review Research |
| title | Power-law entanglement growth from typical product states |
| title_full | Power-law entanglement growth from typical product states |
| title_fullStr | Power-law entanglement growth from typical product states |
| title_full_unstemmed | Power-law entanglement growth from typical product states |
| title_short | Power-law entanglement growth from typical product states |
| title_sort | power law entanglement growth from typical product states |
| url | http://doi.org/10.1103/PhysRevResearch.1.033067 |
| work_keys_str_mv | AT talialmlezama powerlawentanglementgrowthfromtypicalproductstates AT davidjluitz powerlawentanglementgrowthfromtypicalproductstates |