Symmetry Properties of the Ring Heisenberg Hamiltonian and New Sum Rule for Its Energy Eigenvalues

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概要

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• Employing the method of a symmetry lowering (from the permutation group P_n to the dihedral group C_<nv>), the eigenstates of the ring Heisenberg Hamiltonian H=-2JΣ^^n__<i=1>S_i・S_<i+1> are classified not only by total spin S and its z-component M, but also by wave number k=2πL/n, where L= ±0, ±1, ±2, ^, ±p for n=2p+1 or 2p. By the characters of irreducible representation of P_n and C_<nv>, we express the sum of the energy eigenvalues at fixed S, M and L, together with the number of the eigenstates contained in this sum. With respect to the spin configurations in the ring, it is revealed that there exist invariant subspaces under all symmetry operations of C-<nv> in the space of the spin-functions specified by M. By connecting this fact with the Wigner coefficients, the eigenfunctions are easily obtained.

• 理論物理学刊行会の論文
• 1980-09-25

著者

• Fujii Katsuhiko

  Okayama University Of Science

関連論文

• Symmetry Properties of the Ring Heisenberg Hamiltonian and New Sum Rule for Its Energy Eigenvalues
• On the Energy Sum Rule of the Ring Heisenberg Hamiltonian

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