Spin chains and combinatorics

Details Spin chains and combinatorics Spin chains and combinatorics

2000-12-08

arxiv.org/abs/cond-mat/0012141v3

J.Phys.A34:3185,2001

Physics

Condensed Matter

Statistical Mechanics

Latex2e, 6 pages

Scientific paper

10.1088/0305-4470/34/14/322

In this letter we continue the investigation of finite XXZ spin chains with periodic boundary conditions and odd number of sites, initiated in paper \cite{S}. 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 {\sc Mathematica} we have found explicitly the corresponding eigenvectors for $N \le 17$. The obtained results support the conjecture of paper \cite{S} 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 wave function components are noticed. It is turned out, for example, that the ratio of the largest component to the least one is equal to the number of the alternating sing matrices.

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