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Fermionic mean-field theory as a tool for studying spin Hamiltonians.
Thomas M Henderson1,2, Brent Harrison3, Ilias Magoulas4
1Department of Chemistry, Rice University, Houston, Texas 77005, USA.
The Journal of Chemical Physics
|December 18, 2024
Summary
This study explores various spin-fermion mappings, including the Jordan-Wigner transformation, to find the most effective method for applying fermionic mean-field theory to spin Hamiltonians like the XXZ model.
Area of Science:
- Quantum mechanics
- Condensed matter physics
- Spin systems
Background:
- The Jordan-Wigner transformation converts spin operators to spinless fermion operators.
- This transformation can simplify interacting spin Hamiltonians into exactly solvable noninteracting fermionic ones.
- Mean-field solutions of resulting fermionic Hamiltonians offer accurate energies and correlations, even for interacting cases.
Purpose of the Study:
- To investigate and compare different spin-fermion mapping techniques.
- To determine the most effective mapping for applying fermionic mean-field theory to spin Hamiltonians.
- To analyze the utility of these mappings on specific models like the XXZ and J1-J2 Heisenberg models.
Main Methods:
- Application of multiple spin-fermion transformation techniques.
- Analysis of the XXZ and J1-J2 Heisenberg models.
- Study of the pairing or reduced Bardeen-Cooper-Schrieffer Hamiltonian.
Main Results:
- Comparison of the effectiveness of various spin-fermion mappings.
- Identification of the most suitable mapping for fermionic mean-field analysis of spin models.
- Evaluation of the performance of different mappings on selected quantum models.
Conclusions:
- Certain spin-fermion mappings are more advantageous than others for fermionic mean-field theory.
- The choice of mapping significantly impacts the accuracy and solvability of spin Hamiltonian studies.
- This research provides guidance for selecting optimal transformations in condensed matter theory.
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