We present a new quantum molecular dynamics (MD) method where the electronic structure and atomic forces are solved by a real-space dynamical mean-field theory (DMFT). Contrary to most quantum MD methods that are based on effective single-particle wave functions, the DMFT approach is able to describe correlation-induced Mott metal-insulator transitions and the associated incoherent electronic excitations in an atomic liquid. We apply the DMFT-MD method to study Mott transitions in an atomic liquid model which can be viewed as the liquid-state generalization of the Hubbard model. The half-filled Hubbard liquids also provide a minimum model for alkali fluid metals. Our simulations uncover two distinct types of Mott transition depending on the atomic bonding and short-range structures in the electronically delocalized phase. In the first scenario where atoms tend to form dimers, increasing the Hubbard repulsion gives rise to a transition from a molecular insulator to an atomic insulator with a small window of enhanced metallicity in the vicinity of the localization transition. On the other hand, for Hubbard liquids with atoms forming large conducting clusters, the localization of electrons leads to the fragmentation of clusters and is intimately related to the liquid-gas transition of atoms. Implications of our results for metal-insulator transitions in fluid alkali metals are discussed.
We describe a pairing mean-field theory related to the Hartree-Fock-Bogoliubov approach, and apply it to the dynamics of dissociation of a molecular Bose-Einstein condensate into correlated bosonic atom pairs. We also perform the same simulation using two stochastic phase-space techniques for quantum dynamics---the positive-
P representation method and the truncated Wigner method. By comparing the results of our calculations we are able to assess the relative strengths of these theoretical techniques in describing molecular dissociation in one spatial dimension. An important aspect of our analysis is the inclusion of atom-atom interactions, which can be problematic for the positive-
P method. We find that the truncated Wigner method mostly agrees with the positive-
P simulations, but can be simulated for significantly longer times. The pairing mean-field theory results diverge from the quantum dynamical methods after relatively short times.
We present a vibrational dynamical mean-field theory (VDMFT) of the dynamics of atoms in solids with anharmonic interactions. Like other flavors of DMFT, VDMFT maps the dynamics of a periodic anharmonic lattice of atoms onto those of a self-consistently defined impurity problem with local anharmonicity and coupling to a bath of harmonic oscillators. VDMFT is exact in the harmonic and molecular limits, nonperturbative systematically improvable through its cluster extensions, usable with classical or quantum impurity solvers (depending on the importance of nuclear quantum effects) and can be combined with existing low-level diagrammatic theories of anharmonicity. When tested on models of anharmonic optical and acoustic phonons; we find that classical VDMFT gives good agreement with classical molecular dynamics, including the temperature dependence of phonon frequencies and lifetimes. Using a quantum impurity solver, signatures of nuclear quantum effects are observed at low temperatures. We test the description of nonlocal anharmonicity via cellular VDMFT and the combination with self-consistent phonon (SCPH) theory, yielding the powerful SCPH
+ VDMFT approach.