Measurement-Induced Phase Transitions in the Dynamics of Entanglement
© 2019 authors. Published by the American Physical Society. We define dynamical universality classes for many-body systems whose unitary evolution is punctuated by projective measurements. In cases where such measurements occur randomly at a finite rate p for each degree of freedom, we show that the...
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| Format: | Article |
| Language: | English |
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American Physical Society (APS)
2021
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| Online Access: | https://hdl.handle.net/1721.1/136403 |
| _version_ | 1826213923669409792 |
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| author | Skinner, Brian Ruhman, Jonathan Nahum, Adam |
| author_facet | Skinner, Brian Ruhman, Jonathan Nahum, Adam |
| author_sort | Skinner, Brian |
| collection | MIT |
| description | © 2019 authors. Published by the American Physical Society. We define dynamical universality classes for many-body systems whose unitary evolution is punctuated by projective measurements. In cases where such measurements occur randomly at a finite rate p for each degree of freedom, we show that the system has two dynamical phases: "entangling" and "disentangling." The former occurs for p smaller than a critical rate pc and is characterized by volume-law entanglement in the steady state and "ballistic" entanglement growth after a quench. By contrast, for p>pc the system can sustain only area-law entanglement. At p=pc the steady state is scale invariant, and in 1+1D, the entanglement grows logarithmically after a quench. To obtain a simple heuristic picture for the entangling-disentangling transition, we first construct a toy model that describes the zeroth Rényi entropy in discrete time. We solve this model exactly by mapping it to an optimization problem in classical percolation. The generic entangling-disentangling transition can be diagnosed using the von Neumann entropy and higher Rényi entropies, and it shares many qualitative features with the toy problem. We study the generic transition numerically in quantum spin chains and show that the phenomenology of the two phases is similar to that of the toy model but with distinct "quantum" critical exponents, which we calculate numerically in 1+1D. We examine two different cases for the unitary dynamics: Floquet dynamics for a nonintegrable Ising model, and random circuit dynamics. We obtain compatible universal properties in each case, indicating that the entangling-disentangling phase transition is generic for projectively measured many-body systems. We discuss the significance of this transition for numerical calculations of quantum observables in many-body systems. |
| first_indexed | 2024-09-23T15:56:59Z |
| format | Article |
| id | mit-1721.1/136403 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:56:59Z |
| publishDate | 2021 |
| publisher | American Physical Society (APS) |
| record_format | dspace |
| spelling | mit-1721.1/1364032022-04-01T16:26:05Z Measurement-Induced Phase Transitions in the Dynamics of Entanglement Skinner, Brian Ruhman, Jonathan Nahum, Adam © 2019 authors. Published by the American Physical Society. We define dynamical universality classes for many-body systems whose unitary evolution is punctuated by projective measurements. In cases where such measurements occur randomly at a finite rate p for each degree of freedom, we show that the system has two dynamical phases: "entangling" and "disentangling." The former occurs for p smaller than a critical rate pc and is characterized by volume-law entanglement in the steady state and "ballistic" entanglement growth after a quench. By contrast, for p>pc the system can sustain only area-law entanglement. At p=pc the steady state is scale invariant, and in 1+1D, the entanglement grows logarithmically after a quench. To obtain a simple heuristic picture for the entangling-disentangling transition, we first construct a toy model that describes the zeroth Rényi entropy in discrete time. We solve this model exactly by mapping it to an optimization problem in classical percolation. The generic entangling-disentangling transition can be diagnosed using the von Neumann entropy and higher Rényi entropies, and it shares many qualitative features with the toy problem. We study the generic transition numerically in quantum spin chains and show that the phenomenology of the two phases is similar to that of the toy model but with distinct "quantum" critical exponents, which we calculate numerically in 1+1D. We examine two different cases for the unitary dynamics: Floquet dynamics for a nonintegrable Ising model, and random circuit dynamics. We obtain compatible universal properties in each case, indicating that the entangling-disentangling phase transition is generic for projectively measured many-body systems. We discuss the significance of this transition for numerical calculations of quantum observables in many-body systems. 2021-10-27T20:35:12Z 2021-10-27T20:35:12Z 2019 2019-10-22T15:34:50Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/136403 en 10.1103/physrevx.9.031009 Physical Review X Creative Commons Attribution 4.0 International license https://creativecommons.org/licenses/by/4.0/ application/pdf American Physical Society (APS) APS |
| spellingShingle | Skinner, Brian Ruhman, Jonathan Nahum, Adam Measurement-Induced Phase Transitions in the Dynamics of Entanglement |
| title | Measurement-Induced Phase Transitions in the Dynamics of Entanglement |
| title_full | Measurement-Induced Phase Transitions in the Dynamics of Entanglement |
| title_fullStr | Measurement-Induced Phase Transitions in the Dynamics of Entanglement |
| title_full_unstemmed | Measurement-Induced Phase Transitions in the Dynamics of Entanglement |
| title_short | Measurement-Induced Phase Transitions in the Dynamics of Entanglement |
| title_sort | measurement induced phase transitions in the dynamics of entanglement |
| url | https://hdl.handle.net/1721.1/136403 |
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