Using Local Operator Fluctuations to Identify Wave Function Improvements

A method is developed that allows analysis of quantum Monte Carlo simulations to identify errors in trial wave functions. The purpose of this method is to allow for the systematic improvement of variational wave functions by identifying degrees of freedom that are not well-described by an initial trial state. We provide proof of concept implementations of this method by identifying the need for a Jastrow correlation factor, and implementing a selected multi-determinant wave function algorithm for small dimers that systematically decreases the variational energy. Selection of the two-particle excitations is done using quantum Monte Carlo within the presence of a Jastrow correlation factor, and without the need to explicitly construct the determinants. We also show how this technique can be used to design compact wave functions for transition metal systems. This method may provide a route to analyze and systematically improve descriptions of complex quantum systems in a scalable way.

Ground state of doped cuprates from first principles quantum Monte Carlo calculations

The author reports on new high-fidelity simulations of charge carriers in the high-T$_c$ cuprate materials using quantum Monte Carlo techniques applied to the first principles Hamiltonian. With this high accuracy technique, the doped ground state is found to be a spin polaron, in which charge is localized through a strong interaction with the spin. This spin polaron has calculated properties largely similar to the phenomenology of the cuprates, and may be the object which forms the Fermi surface and charge inhomogeneity in these materials. The spin polaron has some unique features that should be visible in X-ray, EELS, and neutron experiments. The results contained in this paper comprise an accurate first principles derived paradigm from which to study superconductivity in the cuprates.

Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions

We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio Quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding (AIDMD). For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard $U^{*}/t$ to be $1.3 pm 0.2$, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large scale calculations using techniques designed for lattice models.

Computation of the correlated metal-insulator transition in vanadium dioxide from first principles

Vanadium dioxide(VO$_2$) is a paradigmatic example of a strongly correlated system that undergoes a metal-insulator transition at a structural phase transition. To date, this transition has necessitated significant post-hoc adjustments to theory in order to be described properly. Here we report standard state-of-the-art first principles quantum Monte Carlo (QMC) calculations of the structural dependence of the properties of VO$_2$. Using this technique, we simulate the interactions between electrons explicitly, which allows for the metal-insulator transition to naturally emerge, importantly without ad-hoc adjustments. The QMC calculations show that the structural transition directly causes the metal-insulator transition and a change in the coupling of vanadium spins. This change in the spin coupling results in a prediction of a momentum-independent magnetic excitation in the insulating state. While two-body correlations are important to set the stage for this transition, they do not change significantly when VO$_2$ becomes an insulator. These results show that it is now possible to account for electron correlations in a quantitatively accurate way that is also specific to materials.

A microscopic description of light induced defects in amorphous silicon solar cells

Using a combination of quantum and classical computational approaches, we model the electronic structure in amorphous silicon in order gain understanding of the microscopic atomic configurations responsible for light induced degradation of solar cells. We demonstrate that regions of strained silicon bonds could be as important as dangling bonds for creating traps for charge carriers. Further, our results show that defects are preferentially formed when a region in the amorphous silicon contains a hole and a light-induced excitation. These results agree with the puzzling dependencies on temperature, time, and pressure observed experimentally.