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Strong-weak duality via Jordan-Wigner transformation: Using fermionic methods for strongly correlated su(2) spin
Thomas M Henderson1, Guo P Chen1, Gustavo E Scuseria1
1Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA.
The Journal of Chemical Physics
|November 22, 2022
Summary
The Jordan-Wigner transformation simplifies strong correlations when mapping spins to fermions, aiding complex quantum system analysis. This method offers a more tractable approach for solving challenging spin problems.
Area of Science:
- Quantum mechanics
- Condensed matter physics
- Computational chemistry
Background:
- The Jordan-Wigner transformation reveals a duality between su(2) spin algebras and fermionic algebras.
- Understanding and mitigating strong correlation effects is crucial for solving complex quantum many-body problems.
Purpose of the Study:
- To investigate the impact of the Jordan-Wigner transformation on the strength of correlations in spin systems.
- To assess the utility of the transformed Hamiltonian for addressing challenging spin problems using computational methods.
Main Methods:
- Qualitative arguments and numerical evidence were employed.
- The Hartree-Fock approximation was applied to the transformed Hamiltonian.
- Analysis included 1D and 2D XXZ and J1-J2 Heisenberg models.
Main Results:
- Mapping spins to fermions via the Jordan-Wigner transformation weakens strong correlation.
- This weakening is attributed to the rank reduction of spin shift terms.
- The transformed fermionic Hamiltonian exhibits reduced complexity in critical phase diagram regions.
Conclusions:
- The Jordan-Wigner transformation provides a more manageable fermionic representation of spin systems.
- This approach simplifies the study of strongly correlated spin models, offering a better starting point for quantum chemistry methods.
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