Parent Hamiltonians of Jastrow wavefunctions

We find the complete family of many-body quantum Hamiltonians with ground-state of Jastrow form involving the pairwise product of a pair function in an arbitrary spatial dimension. The parent Hamiltonian generally includes a two-body pairwise potential as well as a three-body potential. We thus gene...

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Autor principal:	Mathieu Beau, Adolfo del Campo
Formato:	article
Lenguaje:	EN
Publicado:	SciPost 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/c365c61fd30f4f9ba4b6eff16cf8ff39
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id	oai:doaj.org-article:c365c61fd30f4f9ba4b6eff16cf8ff39
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spelling	oai:doaj.org-article:c365c61fd30f4f9ba4b6eff16cf8ff392021-11-18T17:58:58ZParent Hamiltonians of Jastrow wavefunctions2666-936610.21468/SciPostPhysCore.4.4.030https://doaj.org/article/c365c61fd30f4f9ba4b6eff16cf8ff392021-11-01T00:00:00Zhttps://scipost.org/SciPostPhysCore.4.4.030https://doaj.org/toc/2666-9366We find the complete family of many-body quantum Hamiltonians with ground-state of Jastrow form involving the pairwise product of a pair function in an arbitrary spatial dimension. The parent Hamiltonian generally includes a two-body pairwise potential as well as a three-body potential. We thus generalize the Calogero-Marchioro construction for the three-dimensional case to arbitrary spatial dimensions. The resulting family of models is further extended to include a one-body term representing an external potential, which gives rise to an additional long-range two-body interaction. Using this framework, we provide the generalization to an arbitrary spatial dimension of well-known systems such as the Calogero-Sutherland and Calogero-Moser models. We also introduce novel models, generalizing the McGuire many-body quantum bright soliton solution to higher dimensions and considering ground-states which involve e.g., polynomial, Gaussian, exponential, and hyperbolic pair functions. Finally, we show how the pair function can be reverse-engineered to construct models with a given potential, such as a pair-wise Yukawa potential, and to identify models governed exclusively by three-body interactions.Mathieu Beau, Adolfo del CampoSciPostarticlePhysicsQC1-999ENSciPost Physics Core, Vol 4, Iss 4, p 030 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Mathieu Beau, Adolfo del Campo Parent Hamiltonians of Jastrow wavefunctions
description	We find the complete family of many-body quantum Hamiltonians with ground-state of Jastrow form involving the pairwise product of a pair function in an arbitrary spatial dimension. The parent Hamiltonian generally includes a two-body pairwise potential as well as a three-body potential. We thus generalize the Calogero-Marchioro construction for the three-dimensional case to arbitrary spatial dimensions. The resulting family of models is further extended to include a one-body term representing an external potential, which gives rise to an additional long-range two-body interaction. Using this framework, we provide the generalization to an arbitrary spatial dimension of well-known systems such as the Calogero-Sutherland and Calogero-Moser models. We also introduce novel models, generalizing the McGuire many-body quantum bright soliton solution to higher dimensions and considering ground-states which involve e.g., polynomial, Gaussian, exponential, and hyperbolic pair functions. Finally, we show how the pair function can be reverse-engineered to construct models with a given potential, such as a pair-wise Yukawa potential, and to identify models governed exclusively by three-body interactions.
format	article
author	Mathieu Beau, Adolfo del Campo
author_facet	Mathieu Beau, Adolfo del Campo
author_sort	Mathieu Beau, Adolfo del Campo
title	Parent Hamiltonians of Jastrow wavefunctions
title_short	Parent Hamiltonians of Jastrow wavefunctions
title_full	Parent Hamiltonians of Jastrow wavefunctions
title_fullStr	Parent Hamiltonians of Jastrow wavefunctions
title_full_unstemmed	Parent Hamiltonians of Jastrow wavefunctions
title_sort	parent hamiltonians of jastrow wavefunctions
publisher	SciPost
publishDate	2021
url	https://doaj.org/article/c365c61fd30f4f9ba4b6eff16cf8ff39
work_keys_str_mv	AT mathieubeauadolfodelcampo parenthamiltoniansofjastrowwavefunctions
_version_	1718420751174860800

Parent Hamiltonians of Jastrow wavefunctions

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