# A complete quasiclassical map for the dynamics of interacting fermions

## TL;DR

This paper introduces a comprehensive classical mapping approach for simulating the dynamics of interacting fermionic systems, accurately capturing quantum effects and extending to complex observables.

## Contribution

It develops a complete quasiclassical map that preserves quantum dynamics for fermions, including two-body interactions, with a self-consistent quantization scheme.

## Key findings

- Accurately describes quantum impurity dynamics in Coulomb blockade regime
- Works effectively at both low and high temperatures
- Uses a novel importance sampling method to improve efficiency

## Abstract

We present a strategy for mapping the dynamics of a fermionic quantum system to a set of classical dynamical variables. The approach is based on imposing the correspondence relation between the commutator and the Poisson bracket, preserving Heisenberg's equation of motion for one-body operators. In order to accommodate the effect of two-body terms, we further impose quantization on the spin-dependent occupation numbers in the classical equations of motion, with a parameter that is determined self-consistently. Expectation values for observables are taken with respect to an initial quasiclassical distribution that respects the original quantization of the occupation numbers. The proposed classical map becomes complete under the evolution of quadratic Hamiltonians and is extended for all even order observables. We show that the map provides an accurate description of the dynamics for an interacting quantum impurity model in the coulomb blockade regime, at both low and high temperatures. The numerical results are aided by a novel importance sampling scheme that employs a reference system to reduce significantly the sampling effort required to converge the classical calculations.