On the exact continuous mapping of fermions

Abstract We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the many-fermion problem. We show how our scheme can be used to map a general many-fermion Hamiltonian and then con...

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Autores principales:	Andrés Montoya-Castillo, Thomas E. Markland
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2018
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/628e7a92033e4d25b5390516afd6e41e
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spelling	oai:doaj.org-article:628e7a92033e4d25b5390516afd6e41e2021-12-02T11:41:13ZOn the exact continuous mapping of fermions10.1038/s41598-018-31162-62045-2322https://doaj.org/article/628e7a92033e4d25b5390516afd6e41e2018-08-01T00:00:00Zhttps://doi.org/10.1038/s41598-018-31162-6https://doaj.org/toc/2045-2322Abstract We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the many-fermion problem. We show how our scheme can be used to map a general many-fermion Hamiltonian and then consider two specific models that encode the fundamental physics of many fermionic systems, the Anderson impurity and Hubbard models. We use these models to demonstrate how efficient mappings of these Hamiltonians can be constructed using a judicious choice of index ordering of the fermions. This development provides an alternative exact route to calculate the static and dynamical properties of fermionic systems and sets the stage to exploit the quantum-classical and semiclassical hierarchies to systematically derive methods offering a range of accuracies, thus enabling the study of problems where the fermionic degrees of freedom are coupled to complex anharmonic nuclear motion and spins which lie beyond the reach of most currently available methods.Andrés Montoya-CastilloThomas E. MarklandNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 8, Iss 1, Pp 1-9 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Andrés Montoya-Castillo Thomas E. Markland On the exact continuous mapping of fermions
description	Abstract We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the many-fermion problem. We show how our scheme can be used to map a general many-fermion Hamiltonian and then consider two specific models that encode the fundamental physics of many fermionic systems, the Anderson impurity and Hubbard models. We use these models to demonstrate how efficient mappings of these Hamiltonians can be constructed using a judicious choice of index ordering of the fermions. This development provides an alternative exact route to calculate the static and dynamical properties of fermionic systems and sets the stage to exploit the quantum-classical and semiclassical hierarchies to systematically derive methods offering a range of accuracies, thus enabling the study of problems where the fermionic degrees of freedom are coupled to complex anharmonic nuclear motion and spins which lie beyond the reach of most currently available methods.
format	article
author	Andrés Montoya-Castillo Thomas E. Markland
author_facet	Andrés Montoya-Castillo Thomas E. Markland
author_sort	Andrés Montoya-Castillo
title	On the exact continuous mapping of fermions
title_short	On the exact continuous mapping of fermions
title_full	On the exact continuous mapping of fermions
title_fullStr	On the exact continuous mapping of fermions
title_full_unstemmed	On the exact continuous mapping of fermions
title_sort	on the exact continuous mapping of fermions
publisher	Nature Portfolio
publishDate	2018
url	https://doaj.org/article/628e7a92033e4d25b5390516afd6e41e
work_keys_str_mv	AT andresmontoyacastillo ontheexactcontinuousmappingoffermions AT thomasemarkland ontheexactcontinuousmappingoffermions
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On the exact continuous mapping of fermions

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