Novel topological numbers associated with entangled quantum states

2020 Fiscal Year Final Research Report

• Project/Area Number: 17K05563
• 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: Ibaraki University
• Principal Investigator: Fukui Takahiro 茨城大学, 理工学研究科(理学野), 教授 (10322009)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Keywords: トポロジカル不変量 / チャーン数 / ベリー位相 / トポロジカル絶縁体 / 高次トポロジカル絶縁体 / 量子ホール効果

Outline of Final Research Achievements

We have introduced new topological invariants, called entanglement Chern numbers, which are very efficient for describing symmetry-protected topological phases. These new topological invariants allow us to discuss the stability of topological phases quantitatively. We have also shown that for higher-order topological insulators, the entanglement Berry phase is very effective even in the presence of a magnetic field.

Free Research Field

物性理論

Academic Significance and Societal Importance of the Research Achievements

エンタングルメント・ハミルトニアンの基底状態を利用した, 全く新しいトポロジカル不変量を導入したことに大きな意義がある。このようなトポロジカル不変量は, 我々の知る限りは数学分野でも物理分野でもまだ知られていない。