Symmetry Studies of Antiferromagnetic Heisenberg Model

Takashi Ishino, Riichiro Saito, Hiroshi Kamimura

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


A general treatment of the symmetry for quantum spin systems is presented with the use of permutational operators. Symmetry operations which are commutable with a Hamiltonian form the symmetry group. Complete sets of spin functions which are specified by the total spin (Stot) are projected onto the irreducible representations of the symmetry group, using the character table. We show from symmetry consideration that a minimum dimension exists for the ground state of the Heisenberg Hamiltonian with finite N spins. The diagonalization of the Hamiltonian with the use of symmetry consideration can be effectively performed for the complete sets of Stot = 0 by the method proposed in this paper. Numerical results of the ground state and all the excited states of Stot=0 are presented for spin systems up to N=20.

Original languageEnglish
Pages (from-to)3886-3897
Number of pages12
Journaljournal of the physical society of japan
Issue number11
Publication statusPublished - 1990
Externally publishedYes


  • Heisenberg model
  • antiferromagnetism
  • group theory
  • irreducible representation
  • square lattice
  • symmetric group
  • two-dimensional

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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