On the exact continuous mapping of fermions

Montoya-Castillo, Andrés; Markland, Thomas E.

doi:10.1038/s41598-018-31162-6

On the exact continuous mapping of fermions

Journal Article · Tue Aug 28 00:00:00 EDT 2018 · Scientific Reports

DOI:https://doi.org/10.1038/s41598-018-31162-6· OSTI ID:1499991

Montoya-Castillo, Andrés ^[1]; ^[2]

Stanford Univ., CA (United States). Dept. of Chemistry; OSTI
Stanford Univ., CA (United States). Dept. of Chemistry

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.

View Accepted Manuscript (DOE)

Research Organization:: Stanford Univ., CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: SC0014437

OSTI ID:: 1499991

Alternate ID(s):: OSTI ID: 1526793

Journal Information:: Scientific Reports, Journal Name: Scientific Reports Vol. 8; ISSN 2045-2322

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

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