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Published on: May 30, 2014
Hartree-Fock-Bogoliubov theory for number-parity-violating fermionic Hamiltonians.
Thomas M Henderson1,2, Shadan Ghassemi Tabrizi1, Guo P Chen1
1Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA.
Physical Hamiltonians for fermions typically require an even number of operators. This study extends Hartree-Fock-Bogoliubov (HFB) theory to handle an odd number of operators, crucial for Jordan-Wigner transformations in quantum chemistry.
Area of Science:
- Quantum Chemistry
- Condensed Matter Physics
- Theoretical Physics
Background:
- Standard electronic structure theory mandates even fermion operators in physical Hamiltonians.
- The Jordan-Wigner (JW) transformation can introduce odd fermion operators when mapping spin Hamiltonians.
- This parity non-conservation necessitates extensions to standard quantum many-body theories.
Purpose of the Study:
- To extend standard Hartree-Fock-Bogoliubov (HFB) theory to accommodate Hamiltonians with non-conserved particle-number parity.
- To demonstrate a practical application of this generalized HFB theory.
- To improve the study of JW transformations for chemically relevant spin Hamiltonians.
Main Methods:
- Development of a generalized Hartree-Fock-Bogoliubov (HFB) theory.
- Application of coherent states of the SO(2M + 1) Lie group.
- Investigation of the Jordan-Wigner (JW) transformation for spin Hamiltonians.
Main Results:
- A practical framework for HFB theory that handles number-parity-nonconserving Hamiltonians is presented.
- The use of SO(2M + 1) coherent states provides a novel mean-field approach.
- Significant improvements are observed when applying this method to JW-transformed chemical spin Hamiltonians.
Conclusions:
- The generalized HFB theory offers a viable method for systems with parity non-conservation.
- The proposed approach using SO(2M + 1) coherent states is effective for studying JW transformations.
- This work opens new avenues for accurate quantum chemical calculations of spin systems.
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