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Multiscale Modeling

An important aspect of Comscope’s mission is to extend the range of applicability of DMFT. One way we are doing so is using DMFT and allied techniques to provide input for multiscale modeling efforts. Here we discuss two thrusts in this: quantum molecular dynamics and deriving low energy effective Landau-Ginzburg theories of materials.

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Quantum Molecular Dynamics

Gia-Wei Chern, Cristian Batista, Hidemaro Suwa

Quantum molecular dynamics (QMD) simulates the motion of atoms accounting for the interactions between electrons and ions on a quantum mechanical level. It differs from classical molecular dynamics where the concern is the classical motion of ions acted on by a given potential. The main goal of the Comscope’s efforts here has been to develop a strategy for carrying out QMD simulations incorporating electronic correlations through the Gutzwiller approach (and so we have thus named the approach GQMD). The Gutzwiller approach is a general approach in many-body physics (and forms the basis for our G-RISB+LDA code) that is mean-field in nature, incorporating strong electronic correlations while maintaining a single particle picture of a many-body electronic state.

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Cartoon of MD simulation of a single band Hubbard model.

Our primary accomplishment to date in this work has been the development of a GQMD code for a single-band Hubbard model which allowed us to study for the first time the effects of the Mott metal-insulator transition on the static and dynamic properties of the ionic and the electronic components of the system. We have also developed a GQMD code for simulating the liquid phase of the two-orbital Anderson model. The ultimate goal here is to study the dynamics of isostructural phase transitions induced by electronic correlations, such as the α-γ transition of metallic cerium.

The GQMD scheme belongs to the adiabatic quantum MD (or Born-Oppenheimer MD) framework in which the electronic subsystem is assumed to quickly relax to its instantaneous equilibrium of a given ionic configuration. In order to simulate electronically out-of-equilibrium dynamical phenomena, we have also developed non-adiabatic Gutzwiller MD following two different approaches. One is based on the recently proposed time-dependent Gutzwiller approximation method, which introduces coherent dynamics to the slave bosons and quasiparticles in addition to the classical dynamics of ions. Another approach is to combine the GQMD with the non-equilibrium Green’s function (NEGF) for solving the electronic subsystems. 

In the GQMD simulations, the repeated solution of the Gutzwiller self-consistency equations would be prohibitively expensive for large-scale MD simulations of correlated electron materials. Similar issues also occur in density functional theory (DFT)-based quantum MD methods. Machine learning (ML) has proven extremely effective in modeling MD potentials in the context of DFT-MD. We have recently demonstrated that ML model can also emulate the time-consuming Gutzwiller calculation and accurately reproduce results obtained from direct GQMD simulations. Our work also laid the groundwork for realizing large-scale MD simulations for realistic correlated materials using more sophisticated many-body techniques such as quantum Monte Carlo or dynamical mean-field theory (DMFT).

Related Publications

Mott Transition in a Metallic Liquid: Gutzwiller Molecular Dynamics Simulations.
Gia-Wei Chern, Kipton Barros, Cristian D. Batista, Joel D. Kress, and Gabriel Kotliar,
Phys. Rev. Lett. 118, 226401(2017)