|Keywords:||many-body expansion; tensor network|
|Full text PDF:||http://arks.princeton.edu/ark:/88435/dsp011g05ff03c|
A fundamental challenge in quantum physics and chemistry is that accurately describing entangled particles is a high dimensional problem. In the worst case, a required dimension scales exponentially with respect to the number of particles. This thesis describes a set of latest theories and strategies, namely the Density Matrix Renormalization Group (DMRG) ansatz, and the Many-body Expansion(MBE) formalism, to characterize several types of challenging molecular and infinite electronic systems. These methods are designed to efficiently model quantum entanglement in extended electronic systems, but having a polynomial computational cost. The DMRG ansatz is a specification of the quantum tensor network(QTN) in the (quasi)one-dimensional representation. Quantum tensor works originate from mapping the wavefunction of a quantum system onto a tensor network representation. Compared to the traditional linear but exponentially scaled wavefunction representation, quantum tensor networks use non-linear wavefunction representations, and can be engineered to a polynomial computational scaling. Still, it reserves the capability to accurately characterize the true wavefunction. Also, based on this new type of wavefunction representation, further quantities such as analytic gradients, non-adiabatic coupling vectors are developed for quantum chemistry applications. The MBE formalism can be used when the highly correlated wavefunctions of a quantum system too expensive to solve. It splits a total system into many small fragments, and splits total functional such as the total energy to an expansion for distributed computing. With a rapid convergence, this series is further allowed to be truncated when the truncation error is below the required accuracy. Evaluating highly correlated energies of small fragments appearing in MBE terms is feasible. The MBE formalism is an alternative tool to solve total energies for bulk and periodic systems, and it is very straightforward to implement. Advisors/Committee Members: Chain, Garnet (advisor).