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

Arianna Montorsi·Vittorio Penna
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Abstract

We describe the quantum dynamics of the Hubbard model at semi-classical level, by implementing the Time-Dependent Variational Principle (TDVP) procedure on appropriate macroscopic wavefunctions 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 new semi-classical 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 vortex-like ground state phase dynamics is found to take place for U>0 away from half filling. Moreover, it appears that an oscillatory-like 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.

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Arianna Montorsi, Vittorio Penna. 1996-11-28. Dynamics of the Hubbard model: a general approach by time dependent variational principle. https://doi.org/10.1103/physrevb.55.8226

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