Exact Solutions in LowDimensional Problems and Their Application to NonIntegrable Systems
Project/Area Number  07640514 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
物性一般(含基礎論)

Research Institution  Osaka University 
Principal Investigator 
AKUTSU Yasuhiro Osaka University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (10191850)

Project Fiscal Year 
1995 – 1996

Project Status 
Completed(Fiscal Year 1996)

Budget Amount *help 
¥2,300,000 (Direct Cost : ¥2,300,000)
Fiscal Year 1996 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1995 : ¥1,800,000 (Direct Cost : ¥1,800,000)

Keywords  quantum spin chain / Bethe ansatz / exact solution / interface / vicinal surface / numerical renormalization / finite temperature / magnetization process / crystal shape / 量子スピン / ベテ仮説 / 厳密解 / 表面 / 微斜面 / 数値くり込み群 / 有限温度 / 磁化過程 / ベテ仮設 / 数値繰り込み群 / 表面界面 / ラフニング転移 / 結晶平衡形 
Research Abstract 
1.We generalized the "lightconelattice thermal Bethe ansatz" (a method which does not rely on the string hypothesis) in such a way that it can handle systems whose hamiltonians are higherorder conserved quantities of the commuting transfer matrices of twodimensional integrable lattice statistical models. 2.We performed exact analysis of the vicinal surface with general orientation for an integrable surface model. As a result, the universal jump of the gaussian curvature at the facet edge is verified. 3.We studied magnetization process of S = 1 "partially integrable" spin chains which are nonintegrable as a whole but contain integrable subspaces. We found that in some cases the lowestenergy state within the integrable subspace coincides with the system's ground state in a whole range of the magnetic field. The magnetization curve thus obtained is exact. Further, the magnetization curve shows a discontinuity at a field, implying a fieldinduced firstorder phase transition. 4.We exten
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d the productwavefunction renormalization group (PWFRG) method to be applicable to 1D quantum system. Employing the PWFRG,we obtained detailed magnetization curves (MH curves) of 1D quantum antiferromagnets : (1) The critical exponent characterizing the MH curve near the lower critical field is 1/2, but the critical region is so narrow that experiments and other numerical methods can hardly detect the squareroot behavior. (2) We found cusplike singularities in the MH curves, which have been totally unexpected. (3) Comprison with the Betheansatzapproximation calculation shows that the effective deltafunction bose gas picture holds near the critical fields (lower and upper). 5.We applied the above PWFRG to 2D statistical systems, maily interface models. (1) For a nonintegrable interface model, we verified the universal curvature jump of the equilibrium scrystal shape at the roughening temperature. (2) We investigated the validity of the freefermion picture for the terracestepkink model of the vicinal surface. (3) We performed highly reliable calculation of anisotropic step tension on the Si (100) 2 * 1reconstructed surface. Less

Report
(4results)
Research Output
(12results)