Dynamics of the Hubbard model: A general approach by the time-dependent variational principle

Abstract

We describe the quantum dynamics of the Hubbard model at the semiclassical 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 states 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, superconducting, antiferromagnetic and charge-density wave phases and solve the corresponding canonical equations of motion in various cases. Noticeably, a vortexlike ground-state phase dynamics is found to take place for U>0 away from half filling. Moreover, it appears that an oscillatorylike ground-state dynamics survives at the Fermi surface at half filling for any U. The low-energy dynamics is also exactly solved by separating fast and slow variables. The role of the time-dependent phase is shown to be particularly interesting in the ordered phases.