W&M Featured Events
[PAST EVENT] Brandon Kyle Eskridge, Physics - Oral Exam for the Ph.D.
Access & Features
- Open to the public
Brandon Kyle Eskridge, Physics - Final Oral Exam for the Ph.D. Title: Local Embedding and Effective Downfolding in the
Auxiliary-Field Quantum Monte Carlo Method
Abstract: Many interesting phenomena which are observed in materials and molecules are due to strong electron-electron interaction effects, but they create a computational bottleneck for accurate simulations. Exact solutions to the quantum many-electron problem scale exponentially in system size, N. Meanfield-type methods such as density functional theory (DFT) or Hartree-Fock (HF) theory have better (N3-N4) scaling, but are not generally accurate enough in the presence of strong electron-electron interactions. Wavefunction based methods, common in quantum chemistry calculations, are more accurate but scale as high order polynomials N7-N8. The auxiliary-field quantum Monte Carlo (AFQMC) method, which directly computes observables via stochastic sampling, is able to treat the many-electron problem with low-order polynomial cost, similar to mean-field based methods, while maintaining a high degree of accuracy. Still, the computational prefactor is substantial in AFQMC. Local embedding and downfolding is a local correlation approach that aims to extend the system size that can be feasibly treated. A local cluster, in which electrons are fully correlated, is defined and the frozen orbital method is used to construct an effective Hamiltonian which operates only within the local cluster. The approximation is controlled by the separate choice of the spatial size of the active occupied region, Ro, and of the active virtual region, Rv. Absolute energies are seen to converge rapidly in the localization radii, Ro and Rv, and the effective system size that can be treated is greatly extended. The local embedding and downfolding approximation is applied in order to study Ti-capped linear carbon chains within a graphitic environment, a system which would otherwise require significant computational resources on a supercomputer.
Bio: Brandon Kyle Eskridge was born in Cherokee County Oklahoma where he lived for the first months of his life. He then relocated to Aschaffenburg in Bavaria, Germany before finally settling in Alexandria, Virginia at the age of three. He attended James Madison University where he graduated summa cum laude with a B.S. in physics. He received his M.S. from William & Mary in 2015. In Spring 2015, he joined Prof. Henry Krakauer’s research group and began work on solving the Ab. Initio many-electron problem using local correlation methods in the auxiliary-field quantum Monte Carlo method.