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Journal Article

Nonequilibrium Dynamical Mean-Field Theory for Bosonic Lattice Models


Eckstein,  Martin
CFEL, 22761 Hamburg, Germany;
Theory of Correlated Systems out of Equilibrium, Condensed Matter Dynamics Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;

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Strand, H. U., Eckstein, M., & Werner, P. (2015). Nonequilibrium Dynamical Mean-Field Theory for Bosonic Lattice Models. Physical Review X, 5(1): 011038. doi:10.1103/PhysRevX.5.011038.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0028-16BF-2
We develop the nonequilibrium extension of bosonic dynamical mean-field theory and a Nambu real-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory and strong-coupling perturbative approaches, nonequilibrium bosonic dynamical mean-field theory captures not only dynamical transitions but also damping and thermalization effects at finite temperature. We apply the 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 dynamical properties, such as rapid thermalization, trapping in metastable superfluid or normal states, as well as long-lived or strongly damped amplitude oscillations. We summarize our results in nonequilibrium “phase diagrams” that map out the different dynamical regimes.
Bosonic multiparticle systems can Bose condense into a macroscopically occupied quantum state under certain conditions. This phenomenon, which is well understood in weakly interacting systems such as superfluid helium-4, can render quantum effects visible to the naked eye. When cold atoms are confined in an optical lattice, local repulsive interactions suppress the condensate, and the system can undergo a phase transition to a normal phase. The equilibrium properties of this transition are well understood because Monte Carlo simulations make it possible to study a large number of interacting bosons. However, our understanding of the out-of-equilibrium dynamics of these systems is very limited. The time evolution of such systems after perturbations is interesting because it can provide new information about correlation effects, phase-transition dynamics, and thermalization. We present a computationally tractable scheme that allows us to capture the effect of quantum fluctuations on the time evolution of both phases. We develop a “real-time dynamical mean-field formalism” for bosonic lattice systems and use it in quench calculations of the three-dimensional Bose-Hubbard model at finite temperatures, previously intractable from a computational standpoint. We compare the equilibrium phase boundaries of our approximation with exact results and find good agreement. Our formalism captures a rich variety of dynamical behaviors, such as fast thermalization, damped collapse-and-revival oscillations, and the trapping in metastable states. We summarize our results in two “phase diagrams” that map out the dynamical regimes for both a normal and a Bose-condensed initial state. Our simulation approach can be readily generalized and applied to inhomogeneous multicomponent Bose and Bose-Fermi models with more complex local interactions.