Symmetry projection methods in strongly correlated systems
| dc.contributor.advisor | Scuseria, Gustavo E. | en_US |
| dc.creator | Song, Ruiheng | en_US |
| dc.date.accessioned | 2025-01-16T20:00:19Z | en_US |
| dc.date.available | 2025-01-16T20:00:19Z | en_US |
| dc.date.created | 2024-12 | en_US |
| dc.date.issued | 2024-09-30 | en_US |
| dc.date.submitted | December 2024 | en_US |
| dc.date.updated | 2025-01-16T20:00:19Z | en_US |
| dc.description.abstract | Quantum chemistry aims to understand and predict molecular structure and properties by solving the time-independent Schr\"odinger equation within fixed nuclei (Born-Oppenheimer) approximation. The Hamiltonian may have continuous symmetries (e.g., spin) or discrete symmetries (for example, point group). Mean-field wave functions may break some or all of these symmetries. By taking the symmetry-adapted pieces of these broken symmetry states, one can restore the physical character of the wave function while also treating relevant strong correlations. On the other hand, mean-field methods lack dynamic correlation arising from short-range interactions. Still, single-reference methods such as configuration interaction or coupled cluster theory can handle these correlations efficiently. Ideally, we would like to combine these approaches: performing configuration interaction or coupled cluster theory on a broken symmetry reference while restoring the desired symmetries. This work introduces a new approach to integrating symmetry projection and coupled cluster theory. By borrowing techniques from previous research, the new method can restore continuous symmetries like $U$(1) and $SU$(2) and discrete symmetries like point group and time reversal. This method achieves accurate results in challenging systems and has the same computational scaling as traditional coupled cluster theory. Jordan-Wigner transformation is a potent tool in spin models, but its application is challenging due to the inherent strings. The same techniques we use to combine symmetry projection and coupled cluster theory can be used to combine Jordan-Wigner transformation and coupled cluster. The strings are the ' symmetry projection ' operator when constructing the Hartree-Fock and coupled cluster wave functions for a Jordan-Wigner transformed Hamiltonian. Leveraging the method of symmetry projection, we obtain excellent results for both 1-D and 2-D spin models. | en_US |
| dc.format.mimetype | application/pdf | en_US |
| dc.identifier.uri | https://hdl.handle.net/1911/118179 | en_US |
| dc.language.iso | en | en_US |
| dc.subject | quantum chemistry | en_US |
| dc.subject | strong correlation | en_US |
| dc.title | Symmetry projection methods in strongly correlated systems | en_US |
| dc.type | Thesis | en_US |
| dc.type.material | Text | en_US |
| thesis.degree.department | Chemistry | en_US |
| thesis.degree.discipline | Chemistry | en_US |
| thesis.degree.grantor | Rice University | en_US |
| thesis.degree.level | Doctoral | en_US |
| thesis.degree.name | Doctor of Philosophy | en_US |
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