Fermionic Mean-Field Theory as a Tool for Studying Spin Hamiltonians
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915052338020352 |
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| author | Henderson, Thomas M. Harrison, Brent Magoulas, Ilias Necaise, Jason Projansky, Andrew M. Evangelista, Francesco A. Whitfield, James D. Scuseria, Gustavo E. |
| author_facet | Henderson, Thomas M. Harrison, Brent Magoulas, Ilias Necaise, Jason Projansky, Andrew M. Evangelista, Francesco A. Whitfield, James D. Scuseria, Gustavo E. |
| contents | 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 $J_1\text{--}J_2$ Heisenberg models, as well as to the pairing or reduced BCS 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02125 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fermionic Mean-Field Theory as a Tool for Studying Spin Hamiltonians Henderson, Thomas M. Harrison, Brent Magoulas, Ilias Necaise, Jason Projansky, Andrew M. Evangelista, Francesco A. Whitfield, James D. Scuseria, Gustavo E. Strongly Correlated Electrons 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 $J_1\text{--}J_2$ Heisenberg models, as well as to the pairing or reduced BCS 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. |
| title | Fermionic Mean-Field Theory as a Tool for Studying Spin Hamiltonians |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2410.02125 |