Study of nonequilibrium dynamics of integrable quantum systems in association with the relaxation of isolated quantum systems and the dynamical quantum phase transition of the many-body localization

2020 Fiscal Year Final Research Report

• Project/Area Number: 18K03450
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
• Research Institution: Ochanomizu University
• Principal Investigator: Deguchi Tetsuo お茶の水女子大学, 基幹研究院, 教授 (70227544)
• Project Period (FY): 2018-04-01 – 2021-03-31
• Keywords: 可積分量子系 / 孤立量子系 / 多体局在 / 非平衡ダイナミクス

Outline of Final Research Achievements

We have shown finite-size scaling in the many-body localization (MBL) transition and a rigorous method for performing exact time evolution of the spin-1/2 quantum XXZ spin chain. It is a variant of the 1-dim. quantum Heisenberg model where the Z-component of the coupling constant in each nearest neighboring spin pair is given by a parameter Δ. (1) Finite-size scaling behavior among the XXZ anisotropy Δ, the random magnetic field and the system size in the MBL transition was shown. (2) In the two down-spin sector we have shown that at critical values of Δ some bound state solutions of the Bethe ansatz equations collapse into pairs of real solutions. We have derived the Bethe quantum numbers for all the solutions to the Bethe-ansatz equations in the two down-spin sector. Thus, we can exactly perform the time evolution for any given initial state in the two down-spin sector of the spin-1/2 quantum XXZ spin chain, by expressing the initial state as a sum of the Bethe eigenvectors.

Free Research Field

物性基礎論

Academic Significance and Societal Importance of the Research Achievements

孤立量子系の緩和など多体量子系の興味深く精妙なダイナミクスを厳密な方法により研究した。具体的には、XXZ異方性を持つ可積分量子スピン系スピン1/2量子XXZ鎖に対して、以下の２点を示したことである。(1)ランダム性と相互作用の競合が導く多体局在の動的量子相転移において、XXZ異方性変数、ランダム磁場の大きさ、そして系の大きさとの間に新しい有限サイズスケーリングの関係を見出した。(2)下向きスピン２個の場合の実解や複素解のベーテ量子数を厳密に求めた。この結果、下向きスピン２個のとき任意の初期状態からの時間発展を厳密に追跡可能となった。以上の成果は多体量子系や量子技術全般の発展に大きく役立つ。