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A complete quasiclassical map for the dynamics of interacting fermions
Amikam Levy1, Wenjie Dou1, Eran Rabani1
1Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA.
This study introduces a novel classical mapping for fermionic quantum systems, accurately simulating dynamics using classical variables. This method simplifies complex quantum behavior, particularly for interacting impurity models.
Area of Science:
- Quantum mechanics
- Classical mechanics
- Computational physics
Background:
- Simulating fermionic quantum systems is computationally challenging.
- Existing methods often struggle with complex interactions and large systems.
- Developing accurate classical approximations is crucial for understanding quantum dynamics.
Purpose of the Study:
- To develop a strategy for mapping fermionic quantum dynamics to classical variables.
- To preserve fundamental quantum mechanical principles like Heisenberg's equation of motion.
- To accurately describe the dynamics of interacting quantum impurity models.
Main Methods:
- Imposing a correspondence relation between commutator and Poisson bracket.
- Quantizing spin-dependent occupation numbers in classical equations of motion.
- Utilizing an initial quasiclassical distribution for expectation values.
- Employing a novel importance sampling scheme for numerical efficiency.
Main Results:
- A complete classical map is established for quadratic Hamiltonians and extended to even-order observables.
- The map accurately describes the dynamics of an interacting quantum impurity model in the Coulomb blockade regime.
- The method shows accuracy at both low and high temperatures.
- The importance sampling scheme significantly reduces computational effort.
Conclusions:
- The proposed classical mapping offers an accurate and efficient approach to simulating fermionic quantum systems.
- This strategy provides a powerful tool for studying complex quantum phenomena computationally.
- The method is particularly effective for interacting quantum impurity models and related regimes.
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