| Project/Area Number |
11640377
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
物性一般(含基礎論)
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| Research Institution | KOBE UNIVERSITY |
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Principal Investigator |
TONEGAWA Takashi Kobe Univ, Fac of Sci, Prof, 理学部, 教授 (80028167)
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| Co-Investigator(Kenkyū-buntansha) |
MIYASHITA Seiji Univ Tokyo, Grad School of Engin, Prof, 大学院・工学系研究科, 教授 (10143372)
NISHINO Tomotoshi Kobe Univ, Fac of Sci, Lect, 理学部, 講師 (00241563)
KABURAGI Makoto Kobe Univ, Fac of C-C Studies, Prof, 国際文化学部, 教授 (40093504)
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| Project Period (FY) |
1999 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2000: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1999: ¥2,200,000 (Direct Cost: ¥2,200,000)
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| Keywords | quantum mixed spin chain / Spin-1 / 2-1 / 2-1-1 chain / 2-1-3 / 2-1 chain / ground-state phase diagram / Wigner-Eckart theorem / DMRG method / exact diagonalizaiton method / sigle-ion-type anisotropy / Wiger-Eckartの定理 / Lieb-Mattisの定理 / 摂動計算 |
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| Research Abstract |
We have investigated the ground states of the following two kinds of regularly mixed quantum spin chains :
1.Spin-1/2-1/2-1-1 chain in which two S=1/2 and two S=1 spins are arranged alternatively
We have determined the ground-state phase diagram of the spin-1/2-1/2-1-1 chain on an exchange interaction constant plane where the exchange interaction between S=1 spins are antiferromagnetic, employing analytical methods based on the Lieb-Mattis theorem and the Wigner-Eckart theorem as well as numerical methods such as a method of exact diagonalization for finite-size systems and a density-matrix renormalization-group (DMRG) method. We have also calculated the two-spin correlation functions and the string order parameter in the ground states, and have presented a characterization of the phases concerning how the ground state in each phase is represented in the framework of the valence-bond-solid (VBS) picture. These results show that five phases among eleven phases appearing in the ground-stat
… More
e phase diagram are of dimer character, while the remaining six phases are of Haldane character.
Furthermore, we have studied the effect of the uniaxial single-ion-type anisotropy for the S=1 spins on the ground state of the spin-1/2-1/2-1-1 chain. Analyzing, by applying the phenomenological renormalization-group (PRG) method, the numerical data for the energy gap between the ground and first-excited states of finite-size systems calculated by the DMRG method, we have shown that, when the ground state in the case of no anisotropy is of Haldane character, the anisotropy causes a second-order phase transition accompanying the disappearance of the energy gap, as in the case of the uniform S=1 chain.
2.Spin-1/2-1-3/2-1 chain in which the S=1/2, S=1, S=3/2, and S=1 spins are arranged periodically in this order
In a way similar to the case of the above spin-1/2-1/2-1-1 chain, we have determined the ground-state phase diagram of the Spin-1/2-1-3/2-1 chain on an exchange interaction constant plane. We have found a few kinds of ground-state phases, which are all of dimer character. We have compared our result for the phase diagram with Takano's result obtained approximately by mapping the spin Hamiltonian into the nonlinear σ model, and have discussed the applicability of this approximate method. Less
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