2024/10/03 by Thomas M. Henderson, Henderson, Thomas M., Brent Harrison +13 · 2 citations
Physics and Astronomy · Mathematics · #Quantum many-body systems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2410.02125
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 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.