Perturbative analysis from the integrable limits on the dynamics of fractional excitations in quantum spin liquids

2020 Fiscal Year Final Research Report

• Project/Area Number: 16H04026
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Gakushuin University
• Principal Investigator: Udagawa Masafumi 学習院大学, 理学部, 教授 (80431790)
• Project Period (FY): 2016-04-01 – 2021-03-31
• Keywords: 量子スピン液体 / 分数化 / 厳密解 / 動的相関関数 / 幾何学的フラストレーション

Outline of Final Research Achievements

Recently, Kitaev's spin liquid is attracting considerable attention as a platform to perform topological quantum computation. We succeeded in the derivation of exact dynamical magnetic correlation function of this system, which reflect the nature of elementary excitations of this system. On the basis of this exact solution, we derived the dynamical magnetic structure factor, which is essential to interpreting the neutron scattering experiments. We also addressed the hole Green's function, which is applicable to the local detection of non-Abelian anyon, a promising candidate of qubit for quantum computation. We further considered the quantum spin ice system, and developed a general methodology to describe its fractional excitations. We apply this method to address the dynamics of magnetic monopole excitation, and found a phenomenon, which we term as dimensional transmutation. We also found a new class of classical spin liquid emerges out of the attraction between like charges.

Free Research Field

量子スピン液体

Academic Significance and Societal Importance of the Research Achievements

Kitaevスピン液体において、ダイナミクスを正確に記述する動的相関関数の厳密解の導出に成功した成果は、この系がトポロジカル量子計算のプラットフォームとして有望視されていることから非常に意義深い。特に、厳密解に基づくホール相関関数の振る舞いは量子計算の素子である非可換エニオンの局所検出に用いることができ、実際本研究ではSTMを利用した素励起の検出法の提案も行なっている。また、量子スピンアイスの磁気モノポール励起のダイナミクスの記述に成功したことは、量子スピン液体一般に現れる分数励起という新しいクラスの素励起の性質を理解する新しい道筋を開拓したという意味で基礎科学の面から大きな意義を持つ。