A complete quasiclassical map for the dynamics of interacting fermions

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.