The squeezed states of two-mode boson systems are defined through canonical transformation. The defined concept of squeezed boson systems has been applied the Hamiltonian H = gammaS(z)(2) - BSx. The ground-state energy of boson systems is investigated by means of squeezed states. We analyze coherent and squeezed Hamiltonian in the group-theoretic method. It is found that squeezing acts as asymmetry breaking. (C) 2005 Elsevier B.V. All rights reserved.