2017 Fiscal Year Annual Research Report
From Einstein equations to Tensor Networks
| Project/Area Number |
17H06787
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| Research Institution | Kyoto University |
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Principal Investigator |
キャプタ パウエルピオトル 京都大学, 基礎物理学研究所, 特定研究員 (00801747)
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| Project Period (FY) |
2017-08-25 – 2019-03-31
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| Keywords | String Theory / AdS/CFT Correspondence / Tensor Networks / Quantum Entanglement |
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| Outline of Annual Research Achievements |
The first year of the grant realization has been a very fruitful and productive time. I have managed to accomplish several important milestones from the plan and publish them, organize meetings and invite collaborators to Kyoto as well as visit other research institutes for discussions and collaboration. Below, I summarize the achievements in order: 1. I have finished a project on the evolution of entanglement entropy during quantum quenches. 2. With Y. Kusuki, T. Takayanagi and K. Watanabe we investigated the evolution of OTOC correlators in a very important class of conformal field theories known as orbifold CFT. 3. I continued investigating continuous tensor networks from Path Integrals in CFTs. 4. With my visitor Dr. Shinji Hirano, we discovered a new way of computing partition functions in AdS/CFT beyond the large N approximation.
5. I have also managed to finish one of my milestones for 2018 already this year. Namely, formatting and understanding continuous tensor networks for perturbed CFTs. Moreover, I presented my work on various seminars and conferences, visited research institutes in Tokyo University and AEI Potsdam for discussions and invited three researchers for visits to Kyoto: Dr. Alvaro Veil Osorio, Dr. Shinji Hirano and Dr. Fernando Pastawski. Finally I organized two topical workshops at YiTP very closely related to the subject of my grant.
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| Current Status of Research Progress |
Current Status of Research Progress
1: Research has progressed more than it was originally planned.
Reason
The project is in progress. I accomplished most of the first years goals and I am continuing with the original plan.
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| Strategy for Future Research Activity |
In the coming year, I am planning to continue my project with relevant adjustment towards complexity and time dependent tensor networks. As a concrete research plan, I will aim at accomplishing the following goals:
1). Computing Evolution of Complexity in Slow and Fast quenches: I will compute analytically and numerically time evolution of complexity in systems with time dependent mass. This project is in collaboration with the group of Dr. M Heller in Berlin that I visited this year. 2) Computing entanglement in Double Local Quenches. 3) Relating Einstein equations to entanglement: I will study the constraints form (time dependent) Einstein equations on entanglement dynamics. 4) Complexity from Path Integrals. I will formulate and study time dependent tensor networks and their complexity using Nielsen approach as well as compare it with Liouville action prescription. This is already a part of an ongoing project with Dr. J. Magan from Bariloche. Argentina. In the coming year, I plan to realize my project as originally planned and attend a conference “Order from Chaos” at KITP, Santa Barbara, California USA between Dec 10-Dec 14th. For the visit in Europe, I am planning to visit the group of Dr. M. Heller (up to two weeks) in AEI in Potsdam for continuing our collaboration. I would also like to invite Prof. Joan Simon from the University of Edinburgh for discussions (around 3 weeks in September). He is an expert on evolution of entanglement, AdS/CFT as well as higher dimensional SYK models and complexity and would be very beneficial for my project.
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