Theoretical study of seeking for novel topological phenomena and methods of their detection

2019 Fiscal Year Final Research Report

• Project/Area Number: 17K05580
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Ehime University
• Principal Investigator: Nakamura Masaaki 愛媛大学, 理工学研究科(理学系), 准教授 (50339107)
• Project Period (FY): 2017-04-01 – 2020-03-31
• Keywords: トポロジカル物質 / 偏極演算子 / 量子スピン系 / 強相関量子系 / Hubbard模型

Outline of Final Research Achievements

The expected value of the polarization operator in the ground state, in strongly correlated quantum systems is a physical quantity that includes not only the distinction between the conducting phase and the insulating phase, but also the topology of the system in the insulating states. We found that it has a role of amplifying and extracting topological information in various one-dimensional quantum systems when expanded as expected values in terms of excited states. In addition, we analyzed the behavior of the polarization operator near the topological phase transition. Furthermore, we constructed the generalized Hubbard model with the exact ground states on corner sharing lattices related to the topological state. We performed rigorous calculations of quantities related to topological information such as entanglement entropy.

Free Research Field

物性基礎論

Academic Significance and Societal Importance of the Research Achievements

トポロジカル絶縁体の提唱(2005)とその実験的検証(2009)に触発されて、固体物理におけるトポロジカルな物理現象の探究が理論・実験の双方で盛んに行われている。また、既存の物理現象に関してもトポロジカルな観点からの再検討が広く行われ、新たな展開が起きている。特にトポロジカルな物理現象についてはその元祖とも言えるKosteritz- Thouless転移やHaldane予想が2016年のノーベル物理学賞の受賞対象ともなり、この研究分野をさらに発展させようという機運が高まっている。そのような中でトポロジカル相とトポロジカル相転移の特定や検出法に関する基礎付けを行うことは意義深いと考えられる。