Spin chains and combinatorics

被引:121
作者
Razumov, AV [1 ]
Stroganov, YG [1 ]
机构
[1] Inst High Energy Phys, Protvino 142284, Russia
来源
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2001年 / 34卷 / 14期
关键词
D O I
10.1088/0305-4470/34/14/322
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
In this paper we continue the investigation of finite XYZ spin chains with periodic boundary conditions and odd number of sites, initiated in our previous article (Stroganov Yu G 2001 J. Phys. A: Math. Gen. 34 L179-85), As it turned out, for a special value of the asymmetry parameter Delta = -1/2 the Hamiltonian of the system has an eigenvalue, which is exactly proportional to the number of sites E = -3N/2. Using Mathematica we have found explicitly the corresponding eigenvectors for N less than or equal to 17. The obtained results support the conjecture our paper that this special eigenvalue corresponds to the ground state vector. We make a lot of conjectures concerning the correlations of the model. Many remarkable relations between the wavefunction components are noted, It turns out, for example, that the ratio of the largest component to the least one is equal to the number of the alternating sign matrices.
引用
收藏
页码:3185 / 3190
页数:6
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