2019 Fiscal Year Research-status Report
Topological aspects of quantum many-body systems: Symmetry-protected ingappable phases and anomalies
| Project/Area Number |
19K14608
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| Research Institution | The University of Tokyo |
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Principal Investigator |
Hsieh ChangTse 東京大学, カブリ数物連携宇宙研究機構, 特任研究員 (70822146)
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| Project Period (FY) |
2019-04-01 – 2023-03-31
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| Keywords | Quantum anomalies / LSM theorem / SPT phases / Electromagnetic duality / Conformal field theory / Quantum criticality / Quantum spin chains / Majorana fermions |
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| Outline of Annual Research Achievements |
1. One of the works related to my research proposal, "Anomaly Matching and Symmetry-Protected Critical Phases in SU(N) Spin Systems in 1+1 Dimensions", has been accepted and published in Phys. Rev. Lett. after revising the manuscript according to referees' comments and suggestions.
2. In the work "Anomaly of the Electromagnetic Duality of Maxwell Theory", we uncovered a quantum anomaly of the electromagnetic duality of Maxwell theory and showed it is 56 times that of a Weyl fermion, revealing a new feature of the quantum theory of electromagnetism that has not been discussed in the literature. This work has been published in Phys. Rev. Lett. and selected as an Editors' Suggestion, and further introduced by a feature article on Phys.org. A follow-up work "Anomaly inflow and p-form gauge theories", which gives a systematic description of anomalies of p-form gauge theories in various dimensions, has also been completed (on arXiv).
3. In the work "On fermionic minimal models" (on arXiv), we discovered a new family of universality classes, described by a fermionic extension of the Virasoro minimal models of 2d conformal field theories, in 1+1d quantum systems of Majorana fermions. This broadens people’s current understanding of critical phenomena in fermionic systems. Besides providing the theoretical basis of such fermionic minimal models, our technique of constructing explicit Hamiltonians realizing these theories should also be useful, especially for model building, and hence our study can motivate further research along this direction, i.e. on fermionic quantum criticality.
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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
In addition to the works directly related in my research plan about topological aspects of quantum many-body systems, I have also been working on other topics inspired by and extended from the original plan, such as the study of the electromagnetic duality and its anomaly of 3+1d quantum Maxwell theory as well as the investigation of new quantum criticality of 1+1d fermion systems, and have made significant progress (part of the results has been published in Phys. Rev. Lett.).
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| Strategy for Future Research Activity |
1. Extend the studies of symmetry-protected ingappable phases from 1+1d to higher dimensions, using the idea of anomaly matching. One example is to study the deconfined criticality in SU(N) magnets, which should have a dependence on the content of the lattice symmetries (in addition to translation symmetry) on which the systems are defined.
2. Find the anomaly of any possible symmetry of Maxwell theory (including some extensions of Maxwell theory like the all-fermion electrodynamics). It is then a natural task to look for observable consequences for these anomalies. For continuous symmetries, e.g. the SO(2) electromagnetic duality in the source-free Maxwell theory, the corresponding anomalies should be related to anomaly-induced transport and thermodynamics, which might give rise to, e.g. the chiral vortical effects of light.
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| Causes of Carryover |
My original plan for FY2019 included several international trips: attending the ASPEN summer program (USA) in summer 2019, the KITP program (USA) in fall 2019, and the APS March meetings (USA) in spring 2020. However, I changed the travel plan and did not take the above trips. Instead, I arranged some alternative trips, including visiting Academia Sinica and National Sun Yat-sen Univ. (Taiwan), Fudan Univ. (China), and Massachusetts Institute of Technology (USA). This change caused some amount of FY2019 budget unused.
My travel plan for the first-half period of FY2020 is to visit National Tsing Hua Univ. (Taiwan) from April to July 2020 using the FY2020 budget (900,000Yen) combined with the remainder of FY2020 budget (320,000Yen).
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