| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2020: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| 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.
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