Mathematics – Combinatorics
Scientific paper
2009-10-02
Mathematics
Combinatorics
13 pages
Scientific paper
We consider symmetry operators a from the group ring C[S_N] which act on the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We investigate such symmetry operators a which are self-adjoint (in a sence defined in the paper) and which yield consequently observables of the Heisenberg model. We prove the following results: (i) One can construct a self-adjoint idempotent symmetry operator from every irreducible character of every subgroup of S_N. This leads to a big manifold of observables. In particular every commutation symmetry yields such an idempotent. (ii) The set of all generating idempotents of a minimal right ideal R of C[S_N] contains one and only one idempotent which ist self-adjoint. (iii) Every self-adjoint idempotent e can be decomposed into primitive idempotents e = f_1 + ... + f_k which are also self-adjoint and pairwise orthogonal. We give a computer algorithm for the calculation of such decompositions. Furthermore we present 3 additional algorithms which are helpful for the calculation of self-adjoint operators by means of discrete Fourier transforms of S_N. In our investigations we use computer calculations by means of our Mathematica packages PERMS and HRing.
No associations
LandOfFree
Self-adjoint symmetry operators connected with the magnetic Heisenberg ring does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Self-adjoint symmetry operators connected with the magnetic Heisenberg ring, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Self-adjoint symmetry operators connected with the magnetic Heisenberg ring will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-26719