权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Level crossings in integrable finite-size quantum systems with infinite-dimensional symmetry and solvable models in nanoscopic or mesoscopic systems

具有无限维对称性的可积有限尺寸量子系统中的能级交叉以及纳米或介观系统中的可解模型

基本信息

批准号：
17540351
负责人：
DEGUCHI Tetsuo
金额：
$ 2.43万
依托单位：
Ochanomizu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2007
项目状态：
已结题

项目摘要

The spin1/2 XXZ spin chain is one of the most fundamental models among integrable quantum spin systems. When q is an N-th root of unity, the symmetry of the XXZ Hamiltonian is enlarged and it contains the sl(2) loop algebra, which is an infinite-dimensional Lie algebra Here the parameter q is defined by the XXZ coupling Δ by Δ =(q+1/q)/2.We have shown rigorously in some sector that every regular Bethe ansatz eigenvector is a highest weight vector of the sl(2) loop algebra. In order to analyze the spectral degeneracy we have proven a criterion for a finite-dimensional highest weight representation to be irreducible. Furthermore, we have formulated a method for constructing all the possible highest weight representations with the same given highest weight Thus, we have constructed a fundamental algorithm for deriving the spectral degeneracy associated with the sl(2) loop algebra We have also shown the sl(2) loop algebra symmetry for the twisted XXZ spin chains.We have shown that at the superintegrable point of the chiral Potts model the Ising-like spectrum associated with a given regular Bethe state is characterized by a polynomial, which we call the SCP polynomial We have also shown that the SCP polynomial is identical to the Drinfeld polynomial of the degenerate eigenspace associated with the Bethe state. Thus, the sl(2) loop algebra symmetry of the spin-1/2 XXZ chain plays a significant role also in the eigenspectrum of the transfer matrix of the chiral Potts model, which gives a generalization of the 2D Ising model.

自旋1/2XXZ自旋链是可积量子自旋系统中最基本的模型之一。当q是N次单位根时，xxz哈密顿量的对称性被扩大，它包含sl(2)循环代数，其中参数q由xxz耦合Δ由Δ=(q+1/q)/2定义。我们在某些部分严格地证明了每个正则Bethe ansatz特征向量都是sl(2)循环代数的最高权向量。为了分析谱简并性，我们证明了有限维最高权表示不可约的一个判据。我们还证明了扭曲的XXZ自旋链的sl(2)环代数对称性。我们证明了在手征Potts模型的超可积点上，与给定的正则Bethe态有关的类Ising谱由一个多项式来刻画，我们称之为SCP多项式。我们还证明了SCP多项式与与Bethe态有关的简并本征空间的Drinfeld多项式相同。因此，自旋-1/2XXZ链的sl(2)环代数对称性在手征Potts模型的转移矩阵的本征谱中也起着重要作用，这给出了2D Ising模型的推广。