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On the exact continuous mapping of fermions
Andrés Montoya-Castillo1, Thomas E Markland2
1Department of Chemistry, Stanford University, Stanford, California, 94305, USA.
Scientific Reports
|August 30, 2018
Summary
This study introduces a quantum mechanical mapping for fermionic systems, enabling exact calculations of their properties. This method facilitates studying complex quantum-classical interactions previously inaccessible.
Area of Science:
- Quantum mechanics
- Computational physics
- Condensed matter theory
Background:
- Many-fermion systems present significant computational challenges.
- Existing methods struggle with complex interactions between fermionic and other degrees of freedom.
Purpose of the Study:
- To develop a rigorous quantum mechanical mapping of fermionic operators.
- To enable exact calculations of static and dynamical properties for many-fermion systems.
- To provide a foundation for studying coupled quantum-classical systems.
Main Methods:
- Derivation of a quantum mechanical map from fermionic creation/annihilation operators to Cartesian variables.
- Application of the mapping to the Anderson impurity and Hubbard models.
- Optimization of Hamiltonian mappings via fermion index ordering.
Main Results:
- Exact reproduction of the many-fermion problem's matrix structure.
- Demonstrated efficient Hamiltonian mappings for key fermionic models.
- Established a new exact route for calculating fermionic system properties.
Conclusions:
- The developed mapping offers an exact and versatile approach to fermionic system analysis.
- This work paves the way for studying complex quantum-classical phenomena.
- Enables investigations into systems with coupled fermionic, nuclear, spin, and anharmonic dynamics.
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