1999 Fiscal Year Final Research Report Summary
Development of New Numerical Renormalization Group Method and Its Application to Low-Dimensional Phase Transitions
| Project/Area Number |
09640462
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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 | Osaka University |
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Principal Investigator |
AKUTSU Yasuhiro Graduate School of Science, Osaka University Professor, 大学院・理学研究科, 教授 (10191850)
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| Co-Investigator(Kenkyū-buntansha) |
阿久津 泰弘 大阪大学, 大学院・理学研究科, 教授 (10191850)
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| Project Period (FY) |
1997 – 1999
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| Keywords | numerical renormalization / DMRG / PWFRG / quantum spin / vicinal surface / magnetization process / roughening / higher dimension |
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| Research Abstract |
1. (1) For systems with asymmetric transfer matrices, we introduce the "renormalized identity" which allows us to constructed a numerical renormalization scheme where only the symmetric density matrices are involved. (2) We establish a universal asymptotic relation between the density matrix eigenvalue and the number of retained bases. (3) For 3D classical statistical system, we find an explicit construction scheme of local tensor which is an essential building block of the maximum-eigenvalue-state wavefunction of the transfer matrix, establishing a higher-dimensional extension of DMRG. We also show that 2D quantum system can be treated by an anisotropic limit of a 3D classical system.
2. (1) We confirm the anomalous temperature dependence of the step tension in the surface model of NaCl-type crystal. (2) We calculate the anisotropic step tension and the crystal facet shape, from which we verified the validity of the renrmalized free random-walk picture for the step on a surface. (3) We
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study the vicinal surface with adsorption. We find that the attractive inter-step interaction emerges due to the adsorbate density fluctuation, and that there occurs a first-order phase transition due to the inter-step attraction.
3. (1) From the accurate calculation of the M-H curve of the quantum spin chains, we show the validity of the δ-function bose-gas picture near the critical fields. (2) We discover the middle-field cusp singularity in the M-H curve for the S=1/2 spin ladder and S=1 bilinear-biquadratic chain. (3) For the honeycom latttice VBS-type AF spin model, we calculated correlation length and the sublattice magnetization. The S=3/2 bilinear-biquadratic AF spin model, we perform PWFRG-assisted variational calculation based on the product-of-tensors ansatz for the ground-state wavefunction. We find the first-order transition between the Neel and the disordered states. (4) We calculate transverse susceptibility for the 2D Ising-like models, to show that its temperature derivative has the same critical singularity as the specific heat.
4. (1) We establish a method to calculate the free energy and the entropy by the PWFRG/DMRG, and apply it to obtain the zero-point entropy for fully-frustrated antiferromagnets. (2) We study the critical behavior of the 2D Ising-like system with linear defect, to find that the non-universal behavior of the critical exponents persists even if the 4-spin interactions are present. Also, the scaling relations between the defect exponents are confirmed. Less
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