Exact Solutions in Low-Dimensional Problems and Their Application to Non-Integrable Systems

低维问题的精确解及其在不可积系统中的应用

• 批准号: 07640514
• 负责人: AKUTSU Yasuhiro
• 金额: $ 1.47万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07640514/
• 关键词: quantum spin chain; Bethe ansatz; exact solution; interface; vicinal surface; numerical renormalization; finite temperature; magnetization process; crystal shape; 数値繰り込み群; 表面界面; ラフニング転移; 結晶平衡形

1.We generalized the "light-cone-lattice 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 higher-order conserved quantities of the commuting transfer matrices of two-dimensional 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 non-integrable as a whole but contain integrable subspaces. We found that in some cases the lowest-energy 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 field-induced first-order phase transition.4.We exten … More d the product-wavefunction renormalization group (PWFRG) method to be applicable to 1D quantum system. Employing the PWFRG,we obtained detailed magnetization curves (M-H curves) of 1D quantum antiferromagnets : (1) The critical exponent characterizing the M-H 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 square-root behavior. (2) We found cusp-like singularities in the M-H curves, which have been totally unexpected. (3) Comprison with the Bethe-ansatz-approximation calculation shows that the effective delta-function 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 non-integrable interface model, we verified the universal curvature jump of the equilibrium scrystal shape at the roughening temperature. (2) We investigated the validity of the free-fermion picture for the terrace-step-kink model of the vicinal surface. (3) We performed highly reliable calculation of anisotropic step tension on the Si (100) 2 * 1-reconstructed surface. Less

1.我们推广了“光锥晶格热Bethe ansatz”（一种不依赖弦假设的方法），使其能够处理哈密顿量为二维可积晶格统计模型通勤传递矩阵的高阶守恒量的系统。2.我们对可积表面模型的一般方向的邻面进行了精确分析。验证了小平面边缘处高斯曲率的普遍跳跃性。3.研究了S=1“部分可积”自旋链的磁化过程，该自旋链整体不可积，但包含可积子空间。我们发现，在某些情况下，可积子空间内的最低能量状态与整个磁场范围内系统的基态一致。这样得到的磁化曲线是准确的。此外，磁化曲线在场上显示出不连续性，这意味着场引起的一阶相变。4.我们将乘积波函数重正化群（PWFRG）方法扩展到适用于一维量子系统。利用PWFRG，我们获得了一维量子反铁磁体的详细磁化曲线（M-H曲线）：（1）表征下临界场附近M-H曲线的临界指数为1/2，但临界区域很窄，实验和其他数值方法很难检测到平方根行为。 (2) 我们在 M-H 曲线中发现了尖点状奇点，这是完全出乎意料的。 (3)与Bethe-ansatz近似计算比较表明,有效的δ函数玻色气体图像在临界场(下界和上界)附近成立。5.我们将上述PWFRG应用于二维统计系统,主要是界面模型。 (1) 对于不可积界面模型，我们验证了粗化温度下平衡晶体形状的通用曲率跳变。 (2) 我们研究了邻面阶跃扭结模型的自由费米子图的有效性。 (3)我们在Si(100)2*1重建表面上进行了高度可靠的各向异性阶梯张力计算。较少的

项目成果

N.Akutsu: "Quasi-reentrant interface behavior of two-dimensional frustrated Ising models." J.Phys.Soc.Jpn.65・5. 1233-1242 (1996)

N.Akutsu：“二维受挫伊辛模型的准重入界面行为。”J.Phys.Soc.Jpn.65·5（1996）。

佐藤竜太郎: "Curvature Jump at the Facet Edge of a Crystal for Arbitrary Surface Orientation" J.Phys.Soc.Jpn.64. 3593-3597 (1995)

Ryutaro Sato：“任意表面方向的晶体刻面边缘的曲率跳跃”J.Phys.Soc.Jpn.64 (1995)。

N. Akutsu: "Quasi-Reentrant Interface Behavior of Two-Dimensional Frustrated Ising Models" J. Phys. Soc. Jpn.65・5. 1233-1242 (1996)

N. Akutsu：“二维受挫 Ising 模型的准重入界面行为”J. Phys. 65・5 (1996)

K.Sudoh: "Fluctuations of a single step and surface height on vicinal surfaces" J.Phys.Soc.Jpn.65・4. 988-991 (1996)

K.Sudoh：“邻近表面上的单个台阶和表面高度的波动”J.Phys.Soc.Jpn.65・4（1996）。

N. Akutsu: "Step Stiffness and Equilibrium Island Shape of Si(100) Surface : Statistical-Mechanical Calculation with Imaginary Path weight" Surf. Sci.(印刷中). (1997)

N. Akutsu：“Si(100) 表面的阶梯刚度和平衡岛形状：虚路径重量的统计力学计算”Surf。