Towards an efficient first-principles theory of strongly correlated electron materials
Strongly correlated electron materials (SCEM) are a forefront of condensed matter physics, hosting a variety of novel ground states. Our standard theories of materials physics, such as density functional theory, are often not sophisticated enough to accurately solve the Hamiltonian presented by SCEM. More advanced theories, such as the dynamical mean-field theory, can properly capture local Mottphysics, but do so at a large computational expense, precluding indiscriminate application of the method. In this talk, we will present several methodological developments which pave the way towards an efficient first-principles approach to SCEM.
First, we introduce a new variational approach to the quantum many-body problem: the variational discrete action theory (VDAT). VDAT introduces an ansatz for the many-body wave function which is controlled by an integer N, where N = 1 recovers Hartree-Fock, N = 2 recovers the Gutzwiller wave function, and increasing N monotonically approaches the exact solution. The key breakthrough of VDAT is that this wave function ansatz can be exactly evaluated in infinite dimensions with a finite number of operations. In the context of the multi-orbital Hubbard model, a minimal model of SCEM, we will showcase results that demonstrate VDAT at N = 3 has a computational cost comparable to the Gutzwiller approximation while recovering Mott and Hundphysics with remarkable accuracy.
The second development we present is the irreducible derivative approach to computing phonons and their interactions, which is the most efficient finite difference approach allowed by group theory. Phonons and their interactions are necessary for untangling the vibrational component of any observable, which is essential for understanding SCEM. Given that linear response is impractical for most beyond DFT methods, it is critical to pioneer the best possible finite difference method. We showcase the irreducible derivative method by computing phonons, phonon interactions, the interacting phonon Green’s function, and thermal conductivity in a variety of materials, including the Mott insulator uranium dioxide.
Host: Paglione/Butch
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