Budget Amount *help 
¥3,700,000 (Direct Cost : ¥3,700,000)
Fiscal Year 1999 : ¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 1998 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1997 : ¥2,600,000 (Direct Cost : ¥2,600,000)

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 maximumeigenvaluestate wavefunction of the transfer matrix, establishing a higherdimensional 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 NaCltype crystal. (2) We calculate the anisotropic step tension and the crystal facet shape, from which we verified the validity of the renrmalized free randomwalk picture for the step on a surface. (3) We
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study the vicinal surface with adsorption. We find that the attractive interstep interaction emerges due to the adsorbate density fluctuation, and that there occurs a firstorder phase transition due to the interstep attraction. 3. (1) From the accurate calculation of the MH curve of the quantum spin chains, we show the validity of the δfunction bosegas picture near the critical fields. (2) We discover the middlefield cusp singularity in the MH curve for the S=1/2 spin ladder and S=1 bilinearbiquadratic chain. (3) For the honeycom latttice VBStype AF spin model, we calculated correlation length and the sublattice magnetization. The S=3/2 bilinearbiquadratic AF spin model, we perform PWFRGassisted variational calculation based on the productoftensors ansatz for the groundstate wavefunction. We find the firstorder transition between the Neel and the disordered states. (4) We calculate transverse susceptibility for the 2D Isinglike 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 zeropoint entropy for fullyfrustrated antiferromagnets. (2) We study the critical behavior of the 2D Isinglike system with linear defect, to find that the nonuniversal behavior of the critical exponents persists even if the 4spin interactions are present. Also, the scaling relations between the defect exponents are confirmed. Less
