Numerical and Analytical Methods in Low-Dimensional Strongly Correlated Quantum Systems
The study of low-dimensional strongly correlated quantum systems lies at the intersection of intricate theoretical models and practical numerical methods, offering deep insights into condensed matter physics. This thesis explores the application of various numerical and analytical methods to these s...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2024
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| Online Access: | https://hdl.handle.net/1721.1/157584 |
| _version_ | 1824457885773463552 |
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| author | Peng, Changnan |
| author2 | Metlitski, Maxim A. |
| author_facet | Metlitski, Maxim A. Peng, Changnan |
| author_sort | Peng, Changnan |
| collection | MIT |
| description | The study of low-dimensional strongly correlated quantum systems lies at the intersection of intricate theoretical models and practical numerical methods, offering deep insights into condensed matter physics. This thesis explores the application of various numerical and analytical methods to these systems. It addresses universal behaviors and phase transitions, exemplified by the phenomenon of multiversality. Specifically, the transition from a 1D Luttinger liquid to a charge density wave insulator, characterized by partly Kosterlitz-Thouless transition and partly Ising transition, is analyzed using both analytical renormalization group calculations and numerical density matrix renormalization group simulations. Additionally, the thesis introduces a statistical smoothing spline method to pinpoint transition points systematically. The work extends to quantum dynamics, presenting a generic theoretical framework for analyzing quantum-classical adiabatic dynamics with learning algorithms. A provably efficient adiabatic learning (PEAL) algorithm with favorable scaling properties is developed. The algorithm is numerically validated on the 1D Holstein model, demonstrating its precision in predicting dynamics. Furthermore, the thesis derives a Hamiltonian lattice formulation for the 2+1D compact Maxwell-Chern-Simons theory, providing an analytical solution that aligns with continuum theories and facilitating future numerical applications. Through these explorations, the thesis underscores the complementary roles of numerical and analytical methods in advancing the understanding of complex quantum systems. |
| first_indexed | 2025-02-19T04:17:07Z |
| format | Thesis |
| id | mit-1721.1/157584 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2025-02-19T04:17:07Z |
| publishDate | 2024 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1575842024-11-19T04:17:56Z Numerical and Analytical Methods in Low-Dimensional Strongly Correlated Quantum Systems Peng, Changnan Metlitski, Maxim A. Massachusetts Institute of Technology. Department of Physics The study of low-dimensional strongly correlated quantum systems lies at the intersection of intricate theoretical models and practical numerical methods, offering deep insights into condensed matter physics. This thesis explores the application of various numerical and analytical methods to these systems. It addresses universal behaviors and phase transitions, exemplified by the phenomenon of multiversality. Specifically, the transition from a 1D Luttinger liquid to a charge density wave insulator, characterized by partly Kosterlitz-Thouless transition and partly Ising transition, is analyzed using both analytical renormalization group calculations and numerical density matrix renormalization group simulations. Additionally, the thesis introduces a statistical smoothing spline method to pinpoint transition points systematically. The work extends to quantum dynamics, presenting a generic theoretical framework for analyzing quantum-classical adiabatic dynamics with learning algorithms. A provably efficient adiabatic learning (PEAL) algorithm with favorable scaling properties is developed. The algorithm is numerically validated on the 1D Holstein model, demonstrating its precision in predicting dynamics. Furthermore, the thesis derives a Hamiltonian lattice formulation for the 2+1D compact Maxwell-Chern-Simons theory, providing an analytical solution that aligns with continuum theories and facilitating future numerical applications. Through these explorations, the thesis underscores the complementary roles of numerical and analytical methods in advancing the understanding of complex quantum systems. Ph.D. 2024-11-18T19:12:28Z 2024-11-18T19:12:28Z 2024-09 2024-10-24T16:14:17.827Z Thesis https://hdl.handle.net/1721.1/157584 0000-0002-9331-2614 In Copyright - Educational Use Permitted Copyright retained by author(s) https://rightsstatements.org/page/InC-EDU/1.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Peng, Changnan Numerical and Analytical Methods in Low-Dimensional Strongly Correlated Quantum Systems |
| title | Numerical and Analytical Methods in Low-Dimensional Strongly Correlated Quantum Systems |
| title_full | Numerical and Analytical Methods in Low-Dimensional Strongly Correlated Quantum Systems |
| title_fullStr | Numerical and Analytical Methods in Low-Dimensional Strongly Correlated Quantum Systems |
| title_full_unstemmed | Numerical and Analytical Methods in Low-Dimensional Strongly Correlated Quantum Systems |
| title_short | Numerical and Analytical Methods in Low-Dimensional Strongly Correlated Quantum Systems |
| title_sort | numerical and analytical methods in low dimensional strongly correlated quantum systems |
| url | https://hdl.handle.net/1721.1/157584 |
| work_keys_str_mv | AT pengchangnan numericalandanalyticalmethodsinlowdimensionalstronglycorrelatedquantumsystems |