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Title: Coupled Cluster Downfolding Theory: towards universal many-body algorithms for dimensionality reduction of composite quantum systems in chemistry and materials science

Abstract

Abstract The recently introduced coupled cluster (CC) downfolding techniques for reducing the dimensionality of quantum many-body problems recast the CC formalism in the form of the renormalization procedure allowing, for the construction of effective (or downfolded) Hamiltonians in small-dimensionality sub-space, usually identified with the so-called active space, of the entire Hilbert space. The resulting downfolded Hamiltonians integrate out the external (out-of-active-space) Fermionic degrees of freedom from the internal (in-the-active-space) parameters of the wave function, which can be determined as components of the eigenvectors of the downfolded Hamiltonians in the active space. This paper will discuss the extension of non-Hermitian (associated with standard CC formulations) and Hermitian (associated with the unitary CC approaches) downfolding formulations to composite quantum systems commonly encountered in materials science and chemistry. The non-Hermitian formulation can provide a platform for developing local CC approaches, while the Hermitian one can serve as an ideal foundation for developing various quantum computing applications based on the limited quantum resources. We also discuss the algorithm for extracting the semi-analytical form of the inter-electron interactions in the active spaces.

Authors:
;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1866861
Grant/Contract Number:  
72689; 76213
Resource Type:
Published Article
Journal Name:
Materials Theory
Additional Journal Information:
Journal Name: Materials Theory Journal Volume: 6 Journal Issue: 1; Journal ID: ISSN 2509-8012
Publisher:
Springer Science + Business Media
Country of Publication:
Switzerland
Language:
English

Citation Formats

Bauman, Nicholas P., and Kowalski, Karol. Coupled Cluster Downfolding Theory: towards universal many-body algorithms for dimensionality reduction of composite quantum systems in chemistry and materials science. Switzerland: N. p., 2022. Web. doi:10.1186/s41313-022-00046-8.
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Bauman, Nicholas P., & Kowalski, Karol. Coupled Cluster Downfolding Theory: towards universal many-body algorithms for dimensionality reduction of composite quantum systems in chemistry and materials science. Switzerland. https://doi.org/10.1186/s41313-022-00046-8
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Bauman, Nicholas P., and Kowalski, Karol. Sat . "Coupled Cluster Downfolding Theory: towards universal many-body algorithms for dimensionality reduction of composite quantum systems in chemistry and materials science". Switzerland. https://doi.org/10.1186/s41313-022-00046-8.
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@article{osti_1866861,
title = {Coupled Cluster Downfolding Theory: towards universal many-body algorithms for dimensionality reduction of composite quantum systems in chemistry and materials science},
author = {Bauman, Nicholas P. and Kowalski, Karol},
abstractNote = {Abstract The recently introduced coupled cluster (CC) downfolding techniques for reducing the dimensionality of quantum many-body problems recast the CC formalism in the form of the renormalization procedure allowing, for the construction of effective (or downfolded) Hamiltonians in small-dimensionality sub-space, usually identified with the so-called active space, of the entire Hilbert space. The resulting downfolded Hamiltonians integrate out the external (out-of-active-space) Fermionic degrees of freedom from the internal (in-the-active-space) parameters of the wave function, which can be determined as components of the eigenvectors of the downfolded Hamiltonians in the active space. This paper will discuss the extension of non-Hermitian (associated with standard CC formulations) and Hermitian (associated with the unitary CC approaches) downfolding formulations to composite quantum systems commonly encountered in materials science and chemistry. The non-Hermitian formulation can provide a platform for developing local CC approaches, while the Hermitian one can serve as an ideal foundation for developing various quantum computing applications based on the limited quantum resources. We also discuss the algorithm for extracting the semi-analytical form of the inter-electron interactions in the active spaces.},
doi = {10.1186/s41313-022-00046-8},
journal = {Materials Theory},
number = 1,
volume = 6,
place = {Switzerland},
year = {Sat May 07 00:00:00 EDT 2022},
month = {Sat May 07 00:00:00 EDT 2022}
}
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