Application of Algebraic Combinatorics to Finite Spin Systems

• Authors: W. Florek
• Languages of publication: EN

Abstracts

EN

A finite spin system invariant under a symmetry group G is a very illustrative example of a finite group action on mappings f: X → Y (X is a set of spin carriers, Y contains spin projections for a given spin number s). Orbits and stabilizers are used as additional indices of the symmetry adapted basis. Their mathematical nature does not decrease a dimension of a given eigenproblem, but they label states in a systematic way. It allows construction of general formulas for vectors of symmetry adapted basis and matrix elements of operators commuting with the action of G in the space of states. The special role is played by double cosets, since they label nonequivalent (from the symmetry point of view) matrix elements ãx|H|yã for an operator H between Ising configurations |x〉,|y〉. Considerations presented in this paper should be followed by a detailed discussion of different symmetry groups (e.g.) cyclic or dihedral ones) and optimal implementation of algorithms. The paradigmatic example, i.e. a finite spin system, can be useful in investigations of magnetic macromolecules like Fe_6 or Mn_{12} acetate.

Keywords

EN

02.20.Bb; 75.10.Jm; 75.75.+a

Discipline

• 02.20.Bb: General structures of groups
• 75.10.Jm: Quantized spin models, including quantum spin frustration

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2001
• Volume: 100
• Issue: 1
• Pages: 3-22

Dates

published

2001-07

received

2001-06-11

(unknown)

2001-07-13

Contributors

author

W. Florek

• Institute of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland

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Identifiers

DOI

10.12693/APhysPolA.100.3