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DOE OSTI · 2482096

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

Henderson, Thomas M. [Rice University, Houston, TX (United States); Rice University] (ORCID:0000000243584312)·Harrison, Brent [Dartmouth College, Hanover, NH (United States)] (ORCID:0000000340566888)·Magoulas, Ilias [Emory University, Atlanta, GA (United States)] (ORCID:0000000332529112)·Necaise, Jason [Dartmouth College, Hanover, NH (United States)]·Projansky, Andrew M. [Dartmouth College, Hanover, NH (United States)] (ORCID:0000000252342024)·Evangelista, Francesco A. [Emory University, Atlanta, GA (United States)] (ORCID:0000000279176652)·Whitfield, James D. [Dartmouth College, Hanover, NH (United States); AWS Center for Quantum Computing, Pasadena, CA (United States)] (ORCID:0000000328730622)·Scuseria, Gustavo E. [Rice University, Houston, TX (United States)] (ORCID:0000000246358126)
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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. 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 J 1 –J 2 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.

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75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITYCovariance and correlationCrystal field theoryHamiltonian mechanicsHeisenberg modelHilbert spaceMean field theorySelf consistent field methodsSpin operatorThermodynamic limitWick's theorem

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Henderson, Thomas M. [Rice University, Houston, TX (United States); Rice University] (ORCID:0000000243584312), Harrison, Brent [Dartmouth College, Hanover, NH (United States)] (ORCID:0000000340566888), Magoulas, Ilias [Emory University, Atlanta, GA (United States)] (ORCID:0000000332529112), Necaise, Jason [Dartmouth College, Hanover, NH (United States)], Projansky, Andrew M. [Dartmouth College, Hanover, NH (United States)] (ORCID:0000000252342024), Evangelista, Francesco A. [Emory University, Atlanta, GA (United States)] (ORCID:0000000279176652), Whitfield, James D. [Dartmouth College, Hanover, NH (United States); AWS Center for Quantum Computing, Pasadena, CA (United States)] (ORCID:0000000328730622), Scuseria, Gustavo E. [Rice University, Houston, TX (United States)] (ORCID:0000000246358126). 2024-12-18. Fermionic mean-field theory as a tool for studying spin Hamiltonians. https://doi.org/10.1063/5.0242219

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