Abstract
We discuss analytical approximations to the ground-state phase diagram and the elementary excitations of the cooperative Jahn-Teller model describing strongly correlated spin-boson system on a lattice in various quantum optical systems. Based on the mean-field theory approach we show that the system exhibits quantum magnetic structural phase transition which leads to magnetic ordering of the spins and formation of the bosonic condensates. We determine existing of one gapless Goldstone mode and two gapped amplitude modes inside the symmetry-broken phase.
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