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arXiv:cond-mat/9801074 · Physical Review Letters

Dynamical Mean Field Theory of the Bose-Hubbard Model

Luigi Amico A, Vittorio Penna

Published Mar 9, 1998• 98 citations
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Abstract

Quantum dynamics of the Bose-Hubbard model is investigated through a semiclassical Hamiltonian picture provided by the time-dependent variational principle method. The system is studied within a factorized slow/fast dynamics. The semiclassical requantization procedure allows one to account for the strong quantum nature of the system when $t/U\ensuremath{\ll}1$. The phase diagram is in good agreement with quantum Monte Carlo results and third order strong coupling perturbative expansion.

DOI
10.1103/physrevlett.80.2189

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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.
We calculate the momentum dependent spectral function of the Bose-Hubbard model on a simple cubic lattice in three dimensions within the bosonic dynamical mean-field theory (B-DMFT). The continuous-time quantum Monte Carlo method is used to solve the self-consistent B-DMFT equations together with the maximum entropy method for the analytic continuation to real frequencies. Results for weak, intermediate, and strong interactions are presented. In the limit of weak and strong interactions very good agreement with results obtained by perturbation theory is found. By contrast, at intermediate interactions the results differ significantly, indicating that in this regime perturbative methods fail to describe the dynamics of interacting bosons.
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We develop the nonequilibrium extension of bosonic dynamical mean-field theory and a Nambureal-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory andstrong-coupling perturbative approaches, nonequilibrium bosonic dynamical mean-field theory capturesnot only dynamical transitions but also damping and thermalization effects at finite temperature. We applythe formalism to quenches in the Bose-Hubbard model, starting from both the normal and the Bose-condensed phases. Depending on the parameter regime, one observes qualitatively different dynamicalproperties, such as rapid thermalization, trapping in metastable superfluid or normal states, as well aslong-lived or strongly damped amplitude oscillations. We summarize our results in nonequilibrium“phase diagrams” that map out the different dynamical regimes.