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. Furthermore, 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.
Henderson, Thomas M., et al. "Fermionic mean-field theory as a tool for studying spin Hamiltonians." Journal of Chemical Physics, vol. 161, no. 23, Dec. 2024. https://doi.org/10.1063/5.0242219
Henderson, Thomas M., Harrison, Brent, Magoulas, Ilias, Necaise, Jason, Projansky, Andrew M., Evangelista, Francesco A., Whitfield, James D., & Scuseria, Gustavo E. (2024). Fermionic mean-field theory as a tool for studying spin Hamiltonians. Journal of Chemical Physics, 161(23). https://doi.org/10.1063/5.0242219
Henderson, Thomas M., Harrison, Brent, Magoulas, Ilias, et al., "Fermionic mean-field theory as a tool for studying spin Hamiltonians," Journal of Chemical Physics 161, no. 23 (2024), https://doi.org/10.1063/5.0242219
@article{osti_2482096,
author = {Henderson, Thomas M. and Harrison, Brent and Magoulas, Ilias and Necaise, Jason and Projansky, Andrew M. and Evangelista, Francesco A. and Whitfield, James D. and Scuseria, Gustavo E.},
title = {Fermionic mean-field theory as a tool for studying spin Hamiltonians},
annote = {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. Furthermore, 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.},
doi = {10.1063/5.0242219},
url = {https://www.osti.gov/biblio/2482096},
journal = {Journal of Chemical Physics},
issn = {ISSN 0021-9606},
number = {23},
volume = {161},
place = {United States},
publisher = {American Institute of Physics (AIP)},
year = {2024},
month = {12}}
Proceedings of the 29th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 3https://doi.org/10.1145/3620666.3651371