Spin chains and combinatorics
By A. Razumov, Y. Stroganov. 2000
173 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/ab8260420f0474ef288031263a4f17f6210c6182
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In Algebra and Number Theory
In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- Entanglement entropy of excited states (2009, background): “We mention that for ∆ = 1/2 and N odd, thanks to very peculiar combinatorial properties [45], some exact results are known also for finite chains [46, 47].”