Some remarks on the coherent-state variational approach to nonlinear boson models

Mean-field pictures based on the standard time-dependent variational approach have widely been used in studying nonlinear many-boson systems such as the Bose-Hubbard model. Mean-field schemes relevant to Gutzwiller-like trial ;states vertical bar F >, number-preserving states vertical bar xi > and Glauber-like trial states vertical bar Z > are compared to evidence of specific properties of such schemes. After deriving the Hamiltonian picture relevant to vertical bar Z > from that based on vertical bar F >, the latter is shown exhibiting a Poisson algebra equipped with a Weyl -Heisenberg subalgebra which preludes to the vertical bar Z >-based picture. Then states vertical bar Z > are shown to be a superposition of N-boson states vertical bar xi >, and the similarities/differences between the vertical bar Z >-based and vertical bar xi >-based pictures are discussed. Finally, after proving that the simple, symmetric state vertical bar xi > indeed corresponds to a SU(M) coherent state, a dual version of states vertical bar Z > and vertical bar xi > in terms of momentum-mode operators is discussed together with some applications.