In this article we present new formalism for high-order coupled cluster method (CCM) calculations for "generalized" ground-state expectation values and the excited states of quantum magnetic systems with spin quantum number <$E s~symbol У~1 over 2>. We use high-order CCM to demonstrate spontaneous symmetry breaking in the spin-half <$E J sub 1~-~J sub 2> model for the linear chain using the coupled cluster method (CCM). We show that we are able to reproduce exactly the dimerized ground (ket) state at the Majumdar - Ghosh point (<$E J sub 2 "/" J sub 1~=~1 over 2>) using a Neel model state. We show that the onset of dimerized phase is indicated by a bifurcation of the nearest-neighbour ket- and bra-state correlation coefficients for the nearest-neighbour Neel model state. We show that ground-state energies are in good agreement with the results of exact diagonalizations of finite-length chains across this entire regime (i. e., <$E J sub 1~>>~0> and <$E J sub 2~symbol Г~1 over 2>). The effects of the bifurcation point are also observed for the sublattice magnetization for the nearest-neighbour model state. Finally, we use the new formalism for the excited state in order to obtain the excitation energy as a function of <$E J sub 2 "/" J sub 1> for the nearest-neighbour model state by solving up to the LSUB14 level of approximation. We obtain an extrapolated value for the excited-state energy gap of -0,0036 at <$E J sub 2 "/" J sub 1~=~0,0> and of 0,2310 at <$E J sub 2 "/" J sub 1~=~0,5>. We show that an excitation energy gap opens up at <$E J sub 2 "/" J sub 1~symbol Ы~0,24>, although the gap only becomes large at

<$E J sub 2 "/" J sub 1~symbol Ы~0,4>.

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