Extending the Capability of Classical Quantum Many-Body Methods

Citation

Gao, Yang (2022) Extending the Capability of Classical Quantum Many-Body Methods. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/15dc-sd19. https://resolver.caltech.edu/CaltechTHESIS:01032022-192500728

Abstract

This thesis discusses several topics in extending the capability of conventional quantum many-body methods. The first project focuses on extending quantum chemical methods, namely coupled cluster theory, to the correlated systems in the condensed phase. We consider bulk nickel oxide and manganese oxide, which are two paradigmatic correlated electron materials that pose challenges to traditional density functional theory-based simulation framework. We adapted molecular coupled cluster singles and doubles theory using Gaussian basis sets with translational symmetry and norm-conserving pseudopotential. This allowed us to carry a detailed study on the ground and excited states of the two materials.

The second project investigates numerical optimization techniques for Abelien group symmetric tensor contractions. In many-body quantum simulations, group symmetries in states and operators often lead to block sparse structure in the representing tensors. Exploiting this opportunity can significantly reduce the computation cost and memory footprint in tensor contractions. We consider cyclic group symmetry and introduce an efficient remapping scheme to express the sparse tensor contractions almost fully in terms of dense tensor operations.

The third project is devising a wavefunction-based method for coupled electrons and phonons. We are interested in simulating the interacting electrons and phonons at the same footing using coupled cluster methods. The ground state and excited state of two types of systems are investigated in this work: the Hubbard Holstein model and diamond crystal in ab initio setting.

Finally, the fourth project is to develop a generic framework for tensor network simulation on fermionic systems. Tensor network methods are powerful tools to study strongly correlated physical systems. However, traditionally these methods have been developed with commutative algebraic rules, which are commensurate with bosons but not compatible with anti-symmetric fermions. Our approach encodes the fermion statistics directly in the block sparse tensor backend so the tensors behave just like anti-commuting fermion operators.

Thesis Files