Prof. Masaki Oshikawa is a theorist working in the fields of condensed matter physics and statistical physics. Prof. Oshikawa obtained his PhD from the University of Tokyo in 1995. After a short Research Associateship in the University of Tokyo and a Killam Postdoctoral Fellowship in the University of British Columbia, he joined the Tokyo Institute of Technology as an Associate Professor in 1998. In 2006, Prof. Oshikawa moved to University of Tokyo and was promoted to full Professorship, and has been there since then. He is also affiliated with the Kavli Institute for the Physics and Mathematics of the Universe as a senior scientist.
Prof. Oshikawa is well known for his highly original and fundamental work in topology, dynamics, and order in quantum many body systems and is recognized by numerous awards. He received the 7th Ryogo Kubo Memorial Award from the Inoue Foundation for Science, the SEST Award for Young Scientist from the Society of Electron Spin Science and Technology of Japan, the JSPS Prize from the Japanese Society for the Promotion of Science, and elected Fellow by the American Physical Society.
Most of interacting quantum many-body systems are not exactly solvable, and many of them are still challenging for computational approaches. On the other hand, there are a few rigorous theorems which can be applied to a wide range of systems to limit the possible phases of matter to be realized. A theorem proved by Lieb, Schultz, and Mattis in 1961 apparently did not draw much attention (even by the authors themselves) initially, but has evolved over time to become one of the most important theorems for quantum many-body systems. Under certain conditions, the theorem forbids the system to be in a featureless trivial phase. Thus it gives a useful clue for finding nontrivial topological phases. In this talk, I will review the basics and historical evolution of Lieb-Schultz-Mattis theorem, including some of the recent developments.
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