The dynamics of many-body fermionic systems are important in problems ranging from catalytic reactions at electrochemical surfaces to transport through nanojunctions and offer a prime target for quantum computing applications. Here, we derive the set of conditions under which fermionic operators can be exactly replaced by bosonic operators that render the problem amenable to a large toolbox of dynamical methods while still capturing the correct dynamics of n-body operators. Importantly, our analysis offers a simple guide on how one can exploit these simple maps to calculate nonequilibrium and equilibrium single- and multi-time correlation functions essential in describing transport and spectroscopy. We use this to rigorously analyze and delineate the applicability of simple yet effective Cartesian maps that have been shown to correctly capture the correct fermionic dynamics in select models of nanoscopic transport. We illustrate our analytical results with exact simulations of the resonant level model. Our work provides new insights as to when one can leverage the simplicity of bosonic maps to simulate the dynamics of many-electron systems, especially those where an atomistic representation of nuclear interactions becomes essential.
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7 March 2023
Research Article|
March 07 2023
A derivation of the conditions under which bosonic operators exactly capture fermionic structure and dynamics
Andrés Montoya-Castillo
;
Andrés Montoya-Castillo
a)
(Conceptualization, Formal analysis, Investigation, Methodology, Software, Writing – original draft, Writing – review & editing)
1
Department of Chemistry, University of Colorado Boulder
, Boulder, Colorado 80309, USA
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Thomas E. Markland
Thomas E. Markland
b)
(Conceptualization, Formal analysis, Funding acquisition, Methodology, Writing – original draft, Writing – review & editing)
2
Department of Chemistry, Stanford University
, Stanford, California 94305, USA
b)Author to whom correspondence should be addressed: [email protected]
Search for other works by this author on:
a)
Electronic mail: [email protected]
b)Author to whom correspondence should be addressed: [email protected]
J. Chem. Phys. 158, 094112 (2023)
Article history
Received:
December 13 2022
Accepted:
February 13 2023
Citation
Andrés Montoya-Castillo, Thomas E. Markland; A derivation of the conditions under which bosonic operators exactly capture fermionic structure and dynamics. J. Chem. Phys. 7 March 2023; 158 (9): 094112. https://doi.org/10.1063/5.0138664
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