1538 lines
60 KiB
BibTeX
1538 lines
60 KiB
BibTeX
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@misc{Cejnar_2020,
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||
archiveprefix = {arXiv},
|
||
author = {Pavel Cejnar and Pavel Str{\'a}nsk{\'y} and Michal Macek and Michal Kloc},
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||
date-added = {2020-11-20 09:33:29 +0100},
|
||
date-modified = {2020-11-20 09:33:35 +0100},
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||
eprint = {2011.01662},
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||
primaryclass = {quant-ph},
|
||
title = {Excited-state quantum phase transitions},
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year = {2020}}
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@book{GilmoreBook,
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author = {Gilmore, R.},
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date-added = {2020-11-20 09:31:27 +0100},
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date-modified = {2020-11-20 09:31:51 +0100},
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publisher = {New York, Wiley},
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title = {Catastrophe Theory for Scientists and Engineers},
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year = {1981}}
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@book{SachdevBook,
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author = {Sachdev, S.},
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date-added = {2020-11-20 09:30:52 +0100},
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date-modified = {2020-11-20 09:31:18 +0100},
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publisher = {Cambridge University Press},
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||
title = {Quantum Phase Transitions},
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||
year = {1999}}
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@article{Vojta_2003,
|
||
abstract = {In recent years, quantum phase transitions have attracted the interest of both theorists and experimentalists in condensed matter physics. These transitions, which are accessed at zero temperature by variation of a non-thermal control parameter, can influence the behaviour of electronic systems over a wide range of the phase diagram. Quantum phase transitions occur as a result of competing ground state phases. The cuprate superconductors which can be tuned from a Mott insulating to a d-wave superconducting phase by carrier doping are a paradigmatic example. This review introduces important concepts of phase transitions and discusses the interplay of quantum and classical fluctuations near criticality. The main part of the article is devoted to bulk quantum phase transitions in condensed matter systems. Several classes of transitions will be briefly reviewed, pointing out, e.g., conceptual differences between ordering transitions in metallic and insulating systems. An interesting separate class of transitions is boundary phase transitions where only degrees of freedom of a subsystem become critical; this will be illustrated in a few examples. The article is aimed at bridging the gap between high-level theoretical presentations and research papers specialized in certain classes of materials. It will give an overview on a variety of different quantum transitions, critically discuss open theoretical questions, and frequently make contact with recent experiments in condensed matter physics.},
|
||
author = {Matthias Vojta},
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date-added = {2020-11-20 09:27:07 +0100},
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date-modified = {2020-11-20 09:27:27 +0100},
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doi = {10.1088/0034-4885/66/12/r01},
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journal = {Rep. Prog. Phys.},
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number = {12},
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pages = {2069--2110},
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publisher = {{IOP} Publishing},
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title = {Quantum phase transitions},
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volume = {66},
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year = 2003,
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Bdsk-Url-1 = {https://doi.org/10.1088%2F0034-4885%2F66%2F12%2Fr01},
|
||
Bdsk-Url-2 = {https://doi.org/10.1088/0034-4885/66/12/r01}}
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||
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||
@book{CarrBook,
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date-added = {2020-11-20 09:24:47 +0100},
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date-modified = {2020-11-20 09:25:39 +0100},
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||
doi = {10.1201/b10273},
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||
editor = {Carr, L.},
|
||
publisher = {Boca Raton: CRC Press},
|
||
title = {Understanding Quantum Phase Transitions},
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||
year = {2010},
|
||
Bdsk-Url-1 = {https://doi.org/10.1201/b10273}}
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@article{Ernzerhof_2006,
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author = {M. Ernzerhof},
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doi = {10.1063/1.2348880},
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journal = {J. Chem. Phys.},
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pages = {124104},
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title = {Density functional theory of complex transition densities},
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volume = {125},
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year = {2006},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.2348880}}
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@article{Coulson_1949,
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author = {Prof. C.A. Coulson and Miss I. Fischer},
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date-added = {2020-11-20 09:12:25 +0100},
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date-modified = {2020-11-20 09:18:50 +0100},
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doi = {10.1080/14786444908521726},
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journal = {London, Edinburgh Dublin Philos. Mag. J. Sci.},
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number = {303},
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pages = {386-393},
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publisher = {Taylor & Francis},
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title = {XXXIV. Notes on the molecular orbital treatment of the hydrogen molecule},
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volume = {40},
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year = {1949},
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Bdsk-Url-1 = {https://doi.org/10.1080/14786444908521726}}
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@article{Riss_1993,
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author = {U. V. Riss and H.-D. Meyer},
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date-added = {2020-11-20 09:11:19 +0100},
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date-modified = {2020-11-20 09:11:19 +0100},
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journal = {J. Phys. B},
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pages = {4503},
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title = {{Calculation of resonance energies and widths using the complex absorbing potential method.}},
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volume = {26},
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year = {1993}}
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@article{Moiseyev_1998,
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author = {Nimrod Moiseyev},
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journal = {Phys. Rep.},
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pages = {211},
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title = {{Quantum theory of resonances: calculating energies, widths and cross-sections by complex scaling}},
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volume = {302},
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year = {1998}}
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@article{Taut_1993,
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author = {M. Taut},
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doi = {10.1103/PhysRevA.48.3561},
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journal = {Phys. Rev. A},
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pages = {3561},
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title = {Two electrons in an external oscillator potential: Particular analytic solutions of a Coulomb correlation problem},
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volume = {48},
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year = {1993},
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Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.48.3561}}
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||
@article{Loos_2012,
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author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.},
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date-added = {2020-11-19 22:55:26 +0100},
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date-modified = {2020-11-19 22:55:26 +0100},
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doi = {10.1103/PhysRevLett.108.083002},
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||
file = {/Users/loos/Zotero/storage/D5YVLEB5/34.pdf},
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issn = {0031-9007, 1079-7114},
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journal = {Phys. Rev. Lett.},
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language = {en},
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||
month = feb,
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||
number = {8},
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pages = {083002},
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||
title = {Exact {{Wave Functions}} of {{Two}}-{{Electron Quantum Rings}}},
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||
volume = {108},
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||
year = {2012},
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||
Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.108.083002}}
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||
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||
@article{Loos_2010e,
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author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M.W.},
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||
date-added = {2020-11-19 22:55:21 +0100},
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||
date-modified = {2020-11-19 22:55:21 +0100},
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||
doi = {10.1080/00268976.2010.508472},
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||
file = {/Users/loos/Zotero/storage/TLWJZ3HQ/25.pdf},
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issn = {0026-8976, 1362-3028},
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||
journal = {Mol. Phys.},
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||
language = {en},
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||
month = oct,
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||
number = {19-20},
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||
pages = {2527-2532},
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||
title = {Excited States of Spherium},
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||
volume = {108},
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||
year = {2010},
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||
Bdsk-Url-1 = {https://doi.org/10.1080/00268976.2010.508472}}
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@article{Lowdin_1955b,
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author = {L\"owdin, Per-Olov},
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||
date-added = {2020-11-19 21:05:53 +0100},
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||
date-modified = {2020-11-19 21:05:59 +0100},
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||
doi = {10.1103/PhysRev.97.1490},
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||
issue = {6},
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||
journal = {Phys. Rev.},
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||
month = {Mar},
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numpages = {0},
|
||
pages = {1490--1508},
|
||
publisher = {American Physical Society},
|
||
title = {Quantum Theory of Many-Particle Systems. II. Study of the Ordinary Hartree-Fock Approximation},
|
||
url = {https://link.aps.org/doi/10.1103/PhysRev.97.1490},
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||
volume = {97},
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||
year = {1955},
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Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRev.97.1490},
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Bdsk-Url-2 = {https://doi.org/10.1103/PhysRev.97.1490}}
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@article{Lowdin_1955c,
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author = {L\"owdin, Per-Olov},
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date-added = {2020-11-19 21:05:01 +0100},
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||
date-modified = {2020-11-19 21:05:15 +0100},
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doi = {10.1103/PhysRev.97.1509},
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issue = {6},
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journal = {Phys. Rev.},
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month = {Mar},
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numpages = {0},
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pages = {1509--1520},
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||
publisher = {American Physical Society},
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||
title = {Quantum Theory of Many-Particle Systems. III. Extension of the Hartree-Fock Scheme to Include Degenerate Systems and Correlation Effects},
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||
url = {https://link.aps.org/doi/10.1103/PhysRev.97.1509},
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volume = {97},
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year = {1955},
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Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRev.97.1509},
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Bdsk-Url-2 = {https://doi.org/10.1103/PhysRev.97.1509}}
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@article{Lowdin_1955a,
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author = {L\"owdin, Per-Olov},
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date-added = {2020-11-19 21:04:31 +0100},
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date-modified = {2020-11-19 21:07:07 +0100},
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doi = {10.1103/PhysRev.97.1474},
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issue = {6},
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journal = {Phys. Rev.},
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month = {Mar},
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numpages = {0},
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pages = {1474--1489},
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||
publisher = {American Physical Society},
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||
title = {Quantum Theory of Many-Particle Systems. I. Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction},
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||
url = {https://link.aps.org/doi/10.1103/PhysRev.97.1474},
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volume = {97},
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year = {1955},
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Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRev.97.1474},
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Bdsk-Url-2 = {https://doi.org/10.1103/PhysRev.97.1474}}
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@article{Mayer_1993,
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||
abstract = {A study is made of the general Hartree---Fock (GHF) method, in which the basic spin-orbitals may be mixtures of functions having α and β spins. The existence of the solutions to the GHF equations has been proven by Lieb and Simon, and the nature of the various types of solutions has been group theoretically classified by Fukutome. Some numerical applications using Gaussian bases are carried out for some simple systems: the beryllium and carbon atoms and the BH molecule. Some GHF solutions of the general Fukutome-type ``torsional spin density waves'' (TSDW) were found.},
|
||
author = {Istv{\'a}n Mayer and Per-Olov L{\"o}wdin},
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date-added = {2020-11-19 09:09:18 +0100},
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date-modified = {2020-11-19 09:09:26 +0100},
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doi = {https://doi.org/10.1016/0009-2614(93)85341-K},
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issn = {0009-2614},
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journal = {Chemical Physics Letters},
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number = {1},
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pages = {1 - 6},
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title = {Some comments on the general Hartree---Fock method},
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url = {http://www.sciencedirect.com/science/article/pii/000926149385341K},
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volume = {202},
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year = {1993},
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/000926149385341K},
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Bdsk-Url-2 = {https://doi.org/10.1016/0009-2614(93)85341-K}}
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@article{Zhang_2004,
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author = {Zhang, Fan and Burke, Kieron},
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date-added = {2020-11-18 21:23:02 +0100},
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doi = {10.1103/PhysRevA.69.052510},
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journal = {Phys. Rev. A},
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pages = {052510},
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title = {Adiabatic connection for near degenerate excited states},
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volume = {69},
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year = {2004},
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Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.69.052510},
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Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevA.69.052510}}
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@article{Gunnarsson_1976,
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author = {Gunnarsson, O. and Lundqvist, B. I.},
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date-added = {2020-11-18 21:22:53 +0100},
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date-modified = {2020-11-18 21:22:53 +0100},
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doi = {10.1103/PhysRevB.13.4274},
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issue = {10},
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journal = {Phys. Rev. B},
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month = {May},
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numpages = {0},
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pages = {4274--4298},
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publisher = {American Physical Society},
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title = {Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism},
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url = {https://link.aps.org/doi/10.1103/PhysRevB.13.4274},
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volume = {13},
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year = {1976},
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Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.13.4274},
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Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.13.4274}}
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@article{Langreth_1975,
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author = {D.C. Langreth and J.P. Perdew},
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date-added = {2020-11-18 21:22:40 +0100},
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date-modified = {2020-11-18 21:22:40 +0100},
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doi = {https://doi.org/10.1016/0038-1098(79)90254-0},
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issn = {0038-1098},
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journal = {Solid State Commun.},
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number = {8},
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pages = {567 - 571},
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title = {The gradient approximation to the exchange-correlation energy functional: A generalization that works},
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url = {http://www.sciencedirect.com/science/article/pii/0038109879902540},
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volume = {31},
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year = {1979},
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/0038109879902540},
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Bdsk-Url-2 = {https://doi.org/10.1016/0038-1098(79)90254-0}}
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@article{Shea_2018,
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author = {J. A. R. Shea and E. Neuscamman},
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date-added = {2020-11-18 21:17:15 +0100},
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date-modified = {2020-11-18 21:17:15 +0100},
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doi = {10.1063/1.5045056},
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journal = {J. Chem. Phys.},
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pages = {081101},
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title = {A mean field platform for excited state quantum chemistry},
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volume = {149},
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year = {2018},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.5045056}}
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@article{Shea_2017,
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author = {Shea, Jacqueline A. R. and Neuscamman, Eric},
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date-added = {2020-11-18 21:17:15 +0100},
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date-modified = {2020-11-18 21:17:15 +0100},
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doi = {10.1021/acs.jctc.7b00923},
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issn = {1549-9618, 1549-9626},
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journal = {J. Chem. Theory Comput.},
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month = dec,
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number = {12},
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pages = {6078-6088},
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title = {Size {{Consistent Excited States}} via {{Algorithmic Transformations}} between {{Variational Principles}}},
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volume = {13},
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year = {2017},
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Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.7b00923}}
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@article{Thom_2008,
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author = {Thom, Alex J. W. and {Head-Gordon}, Martin},
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date-added = {2020-11-18 21:17:05 +0100},
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date-modified = {2020-11-18 21:17:05 +0100},
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||
doi = {10.1103/PhysRevLett.101.193001},
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||
file = {/Users/loos/Zotero/storage/HVKYKGQU/Thom and Head-Gordon - 2008 - Locating Multiple Self-Consistent Field Solutions.pdf},
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issn = {0031-9007, 1079-7114},
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journal = {Phys. Rev. Lett.},
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month = nov,
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number = {19},
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pages = {193001},
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shorttitle = {Locating {{Multiple Self}}-{{Consistent Field Solutions}}},
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title = {Locating {{Multiple Self}}-{{Consistent Field Solutions}}: {{An Approach Inspired}} by {{Metadynamics}}},
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volume = {101},
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year = {2008},
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Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.101.193001}}
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@article{Gilbert_2008,
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author = {A. T. B. Gilbert and N. A. Besley and P. M. W. Gill},
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date-added = {2020-11-18 21:16:52 +0100},
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date-modified = {2020-11-18 21:16:52 +0100},
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doi = {10.1021/jp801738f},
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journal = {J. Phys. Chem. A},
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pages = {13164},
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title = {Self-Consistent Field Calculations of Excited States Using the Maximum Overlap Method {(MOM)}},
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volume = {112},
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year = {2008},
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Bdsk-Url-1 = {https://doi.org/10.1021/jp801738f}}
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@article{Burton_2018,
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||
abstract = {We explore the existence and behavior of holomorphic restricted Hartree-Fock (h-RHF) solutions for two-electron problems. Through algebraic geometry, the exact number of solutions with n basis functions is rigorously identified as 1/2(3n - 1), proving that states must exist for all molecular geometries. A detailed study on the h-RHF states of HZ (STO3G) then demonstrates both the conservation of holomorphic solutions as geometry or atomic charges are varied and the emergence of complex h-RHF solutions at coalescence points. Using catastrophe theory, the nature of these coalescence points is described, highlighting the influence of molecular symmetry. The h-RHF states of HHeH2+ and HHeH (STO-3G) are then compared, illustrating the isomorphism between systems with two electrons and two electron holes. Finally, we explore the h-RHF states of ethene (STO-3G) by considering the $\pi$ electrons as a two-electron problem and employ NOCI to identify a crossing of the lowest energy singlet and triplet states at the perpendicular geometry.},
|
||
author = {Burton, Hugh G. A. and Gross, Mark and Thom, Alex J. W.},
|
||
date-added = {2020-11-18 21:16:36 +0100},
|
||
date-modified = {2020-11-18 21:16:36 +0100},
|
||
doi = {10.1021/acs.jctc.7b00980},
|
||
file = {/Users/loos/Zotero/storage/E9FNMAU8/Burton et al. - 2018 - Holomorphic Hartree--Fock Theory The Nature of Two.pdf},
|
||
issn = {1549-9618, 1549-9626},
|
||
journal = {J. Chem. Theory Comput.},
|
||
month = feb,
|
||
number = {2},
|
||
pages = {607-618},
|
||
shorttitle = {Holomorphic {{Hartree}}\textendash{{Fock Theory}}},
|
||
title = {Holomorphic {{Hartree}}\textendash{{Fock Theory}}: {{The Nature}} of {{Two}}-{{Electron Problems}}},
|
||
volume = {14},
|
||
year = {2018},
|
||
Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.7b00980}}
|
||
|
||
@article{Burton_2016,
|
||
author = {H. G. A. Burton and A. J. W. Thom},
|
||
date-added = {2020-11-18 21:16:36 +0100},
|
||
date-modified = {2020-11-18 21:16:36 +0100},
|
||
doi = {10.1021/acs.jctc.5b01005},
|
||
journal = {J. Chem. Theory Comput.},
|
||
pages = {167},
|
||
title = {Holomorphic {Hartree--Fock} Theory: An Inherently Multireference Approach},
|
||
volume = {12},
|
||
year = {2016},
|
||
Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.5b01005}}
|
||
|
||
@article{Carrascal_2015,
|
||
abstract = {This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of density functional theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy\textendash{}Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green's function, demonstrating the `failure' of the Kohn\textendash{}Sham (KS) method to reproduce the fundamental gap. We perform benchmark calculations of the occupation and components of the KS potentials, the correlation kinetic energies, and the adiabatic connection. We test several approximate functionals (restricted and unrestricted Hartree\textendash{}Fock and Bethe ansatz local density approximation) to show their successes and limitations. We also discuss and illustrate the concept of the derivative discontinuity. Useful appendices include analytic expressions for density functional energy components, several limits of the exact functional (weak- and strong-coupling, symmetric and asymmetric), various adiabatic connection results, proofs of exact conditions for this model, and the origin of the Hubbard model from a minimal basis model for stretched H2.},
|
||
author = {Carrascal, D J and Ferrer, J and Smith, J C and Burke, K},
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date-added = {2020-11-14 21:44:15 +0100},
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date-modified = {2020-11-14 21:44:15 +0100},
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doi = {10.1088/0953-8984/27/39/393001},
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file = {/Users/loos/Zotero/storage/LRMWNYEQ/Carrascal et al. - 2015 - The Hubbard dimer a density functional case study.pdf},
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issn = {0953-8984, 1361-648X},
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journal = {J. Phys. Condens. Matter},
|
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language = {en},
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month = oct,
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number = {39},
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pages = {393001},
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shorttitle = {The {{Hubbard}} Dimer},
|
||
title = {The {{Hubbard}} Dimer: A Density Functional Case Study of a Many-Body Problem},
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volume = {27},
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year = {2015},
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Bdsk-Url-1 = {https://doi.org/10.1088/0953-8984/27/39/393001}}
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@article{Carrascal_2018,
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abstract = {The asymmetric Hubbard dimer is used to study the density-dependence of the exact frequencydependent kernel of linear-response time-dependent density functional theory. The exact form of the kernel is given, and the limitations of the adiabatic approximation utilizing the exact ground-state functional are shown. The oscillator strength sum rule is proven for lattice Hamiltonians, and relative oscillator strengths are defined appropriately. The method of Casida for extracting oscillator strengths from a frequencydependent kernel is demonstrated to yield the exact result with this kernel. An unambiguous way of labelling the nature of excitations is given. The fluctuation-dissipation theorem is proven for the groundstate exchange-correlation energy. The distinction between weak and strong correlation is shown to depend on the ratio of interaction to asymmetry. A simple interpolation between carefully defined weak-correlation and strong-correlation regimes yields a density-functional approximation for the kernel that gives accurate transition frequencies for both the single and double excitations, including charge-transfer excitations. Many exact results, limits, and expansions about those limits are given in the Appendices.},
|
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author = {Carrascal, Diego J. and Ferrer, Jaime and Maitra, Neepa and Burke, Kieron},
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date-modified = {2020-11-14 21:44:15 +0100},
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doi = {10.1140/epjb/e2018-90114-9},
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pages = {142},
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title = {Linear Response Time-Dependent Density Functional Theory of the {{Hubbard}} Dimer},
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volume = {91},
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year = {2018},
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Bdsk-Url-1 = {https://doi.org/10.1140/epjb/e2018-90114-9}}
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author = {Paw{\l}owski,Filip and Olsen,Jeppe and J{\o}rgensen,Poul},
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title = {Cluster perturbation theory. V. Theoretical foundation for cluster linear target states},
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url = {https://doi.org/10.1063/1.5053627},
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author = {Paw{\l}owski,Filip and Olsen,Jeppe and J{\o}rgensen,Poul},
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@article{Pawlowski_2019b,
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abstract = {For non-Hermitian Hamiltonians with an isolated degeneracy (`exceptional point'), a model for cycling around loops that enclose or exclude the degeneracy is solved exactly in terms of Bessel functions. Floquet solutions, returning exactly to their initial states (up to a constant) are found, as well as exact expressions for the adiabatic multipliers when the evolving states are represented as a superposition of eigenstates of the instantaneous Hamiltonian. Adiabatically (i.e. for slow cycles), the multipliers of exponentially subdominant eigenstates can vary wildly, unlike those driven by Hermitian operators, which change little. These variations are explained as an example of the Stokes phenomenon of asymptotics. Improved (superadiabatic) approximations tame the variations of the multipliers but do not eliminate them.},
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pages = {581--595},
|
||
publisher = {{IOP Publishing}},
|
||
title = {Phase Structure of Interacting Boson Models in Arbitrary Dimension},
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volume = {40},
|
||
year = {2007},
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||
Bdsk-Url-1 = {https://doi.org/10.1088/1751-8113/40/4/001}}
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