Fermionic mean-field theory as a tool for studying spin Hamiltonians

Thomas M Henderson; Brent Harrison; Ilias Magoulas; Jason Necaise; Andrew M Projansky; Francesco A Evangelista; James D Whitfield; Gustavo E Scuseria

doi:10.1063/5.0242219

Fermionic mean-field theory as a tool for studying spin Hamiltonians

J Chem Phys. 2024 Dec 21;161(23):234112. doi: 10.1063/5.0242219.

Authors

Thomas M Henderson^{1

2}, Brent Harrison³, Ilias Magoulas⁴, Jason Necaise³, Andrew M Projansky³, Francesco A Evangelista⁴, James D Whitfield^{3

5}, Gustavo E Scuseria^{1

2}

Affiliations

¹ Department of Chemistry, Rice University, Houston, Texas 77005, USA.
² Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA.
³ Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA.
⁴ Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA.
⁵ AWS Center for Quantum Computing, Pasadena, California 91125, USA.

PMID: 39692486
DOI: 10.1063/5.0242219

Abstract

The Jordan-Wigner transformation permits one to convert spin 1/2 operators into spinless fermion ones, or vice versa. In some cases, it transforms an interacting spin Hamiltonian into a noninteracting fermionic one, which is exactly solved at the mean-field level. Even when the resulting fermionic Hamiltonian is interacting, its mean-field solution can provide surprisingly accurate energies and correlation functions. Jordan-Wigner is, however, only one possible means of interconverting spin and fermionic degrees of freedom. Here, we apply several such techniques to the XXZ and J1-J2 Heisenberg models, as well as to the pairing or reduced Bardeen-Cooper-Schrieffer Hamiltonian, with the aim of discovering which of these mappings is most useful in applying fermionic mean-field theory to the study of spin Hamiltonians.