2018 Fiscal Year Final Research Report
From Einstein equations to Tensor Networks
| Project/Area Number |
17H06787
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2017-08-25 – 2019-03-31
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| Keywords | AdS/CFT / Tensor Networks / Entanglement Dynamics / Complexity / Quantum Quench / Holography / Conformal Field Theory / Quantum Gravity |
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| Outline of Final Research Achievements |
In this project, with my collaborators, I have made 2 major breakthroughs. One was based on exploration of path integral complexity and continuous Tensor Networks in CFTs and their deformations that finally led to the first computation of Entanglement of Purification from CFT. My second line of research was on computational complexity in quantum field theory and understanding its geometric role in AdS/CFT. I managed to give a first definition of geometric complexity in interacting CFTs and showed that if is related to the gravity action introduced long ago by Polyakov.
I also proposed to use circuit complexity as a probe of quantum quenches and, in an exactly solvable setup, demonstrated that it indeed can capture (it is sensitive to) non-trivial information about the evolution process like Kibble-Zurek scaling. All these papers were published in prestigious and very-high impact PRL.
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| Free Research Field |
Theoretical Physics
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| Academic Significance and Societal Importance of the Research Achievements |
My ground-breaking results opened new unexplored paths for research that uses ideas from quantum information, quantum computation and computational complexity in the framework of continuous quantum field theories. In the future I will use them as tools quantum field theories and genuine AdS/CFT.
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