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

Thomas M Henderson1,2, Brent Harrison3, Ilias Magoulas4

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|December 18, 2024
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Summary
This summary is machine-generated.

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.

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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.