DYNAMICS OF THE HUBBARD-MODEL - A GENERAL-APPROACH BY THE TIME-DEPENDENT VARIATIONAL PRINCIPLE

We describe the quantum dynamics of the Hubbard model at the semiclass ical level, by implementing the time-dependent variational principle ( TDVP) procedure on appropriate macroscopic wave functions constructed in terms of SU(2)-coherent states. Within the TDVP procedure, such sta tes turn out to include a time-dependent quantum phase, part of which can be recognized as Berry's phase. We derive two semiclassical model Hamiltonians for describing the dynamics in the paramagnetic, supercon ducting, antiferromagnetic and charge-density wave phases and solve th e corresponding canonical equations of motion in various cases. Notice ably, a vortexlike ground-state phase dynamics is found to take place for U>0 away from half filling. Moreover, it appears that an oscillato rylike ground-state dynamics survives at the Fermi surface at half fil ling for any U. The low-energy dynamics is also exactly solved by sepa rating fast and slow variables. The role of the time-dependent phase i s shown to be particularly interesting in the ordered phases.