Perturbation theory in the complex plane: exceptional points and where to find them
We explore the non-Hermitian extension of quantum chemistry in the complex plane and its link with perturbation theory. We observe that the physics of a quantum system is intimately connected to the position of complex-valued energy singularities, known as exceptional points. After presenting the fu...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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IOP Publishing
2021
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| _version_ | 1797084864158105600 |
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| author | Marie, A Burton, HGA Loos, P-F |
| author_facet | Marie, A Burton, HGA Loos, P-F |
| author_sort | Marie, A |
| collection | OXFORD |
| description | We explore the non-Hermitian extension of quantum chemistry in the complex plane and its link with perturbation theory. We observe that the physics of a quantum system is intimately connected to the position of complex-valued energy singularities, known as exceptional points. After presenting the fundamental concepts of non-Hermitian quantum chemistry in the complex plane, including the mean-field Hartree–Fock approximation and Rayleigh–Schrödinger perturbation theory, we provide a historical overview of the various research activities that have been performed on the physics of singularities. In particular, we highlight seminal work on the convergence behaviour of perturbative series obtained within Møller–Plesset perturbation theory, and its links with quantum phase transitions. We also discuss several resummation techniques (such as Padé and quadratic approximants) that can improve the overall accuracy of the Møller–Plesset perturbative series in both convergent and divergent cases. Each of these points is illustrated using the Hubbard dimer at half filling, which proves to be a versatile model for understanding the subtlety of analytically-continued perturbation theory in the complex plane.
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| first_indexed | 2024-03-07T02:01:05Z |
| format | Journal article |
| id | oxford-uuid:9d616176-9a3e-420b-816d-1685c7847d8d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:01:05Z |
| publishDate | 2021 |
| publisher | IOP Publishing |
| record_format | dspace |
| spelling | oxford-uuid:9d616176-9a3e-420b-816d-1685c7847d8d2022-03-27T00:42:43ZPerturbation theory in the complex plane: exceptional points and where to find them Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:9d616176-9a3e-420b-816d-1685c7847d8dEnglishSymplectic ElementsIOP Publishing2021Marie, ABurton, HGALoos, P-FWe explore the non-Hermitian extension of quantum chemistry in the complex plane and its link with perturbation theory. We observe that the physics of a quantum system is intimately connected to the position of complex-valued energy singularities, known as exceptional points. After presenting the fundamental concepts of non-Hermitian quantum chemistry in the complex plane, including the mean-field Hartree–Fock approximation and Rayleigh–Schrödinger perturbation theory, we provide a historical overview of the various research activities that have been performed on the physics of singularities. In particular, we highlight seminal work on the convergence behaviour of perturbative series obtained within Møller–Plesset perturbation theory, and its links with quantum phase transitions. We also discuss several resummation techniques (such as Padé and quadratic approximants) that can improve the overall accuracy of the Møller–Plesset perturbative series in both convergent and divergent cases. Each of these points is illustrated using the Hubbard dimer at half filling, which proves to be a versatile model for understanding the subtlety of analytically-continued perturbation theory in the complex plane. |
| spellingShingle | Marie, A Burton, HGA Loos, P-F Perturbation theory in the complex plane: exceptional points and where to find them |
| title | Perturbation theory in the complex plane: exceptional points and where to find them
|
| title_full | Perturbation theory in the complex plane: exceptional points and where to find them
|
| title_fullStr | Perturbation theory in the complex plane: exceptional points and where to find them
|
| title_full_unstemmed | Perturbation theory in the complex plane: exceptional points and where to find them
|
| title_short | Perturbation theory in the complex plane: exceptional points and where to find them
|
| title_sort | perturbation theory in the complex plane exceptional points and where to find them |
| work_keys_str_mv | AT mariea perturbationtheoryinthecomplexplaneexceptionalpointsandwheretofindthem AT burtonhga perturbationtheoryinthecomplexplaneexceptionalpointsandwheretofindthem AT loospf perturbationtheoryinthecomplexplaneexceptionalpointsandwheretofindthem |