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Title: 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 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.

Authors:
 [1]; ORCiD logo [1]
  1. Stanford Univ., CA (United States). Dept. of Chemistry
Publication Date:
Research Org.:
Stanford Univ., CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Chemical Sciences, Geosciences & Biosciences Division
OSTI Identifier:
1499991
Alternate Identifier(s):
OSTI ID: 1526793
Grant/Contract Number:  
[SC0014437]
Resource Type:
Accepted Manuscript
Journal Name:
Scientific Reports
Additional Journal Information:
[ Journal Volume: 8]; Journal ID: ISSN 2045-2322
Publisher:
Nature Publishing Group
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; chemical physics; method development; quantum information; theoretical physics

Citation Formats

Montoya-Castillo, Andrés, and Markland, Thomas E. On the exact continuous mapping of fermions. United States: N. p., 2018. Web. doi:10.1038/s41598-018-31162-6.
Montoya-Castillo, Andrés, & Markland, Thomas E. On the exact continuous mapping of fermions. United States. doi:10.1038/s41598-018-31162-6.
Montoya-Castillo, Andrés, and Markland, Thomas E. Tue . "On the exact continuous mapping of fermions". United States. doi:10.1038/s41598-018-31162-6. https://www.osti.gov/servlets/purl/1499991.
@article{osti_1499991,
title = {On the exact continuous mapping of fermions},
author = {Montoya-Castillo, Andrés and Markland, Thomas E.},
abstractNote = {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.},
doi = {10.1038/s41598-018-31162-6},
journal = {Scientific Reports},
number = ,
volume = [8],
place = {United States},
year = {2018},
month = {8}
}

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Figures / Tables:

Figure 1 Figure 1: Index ordering options for the Anderson model.

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