A complete quasiclassical map for the dynamics of interacting fermions

Amikam Levy, Wenjie Dou, Eran Rabani, David T. Limmer

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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.

Original languageEnglish
Article number234112
JournalJournal of Chemical Physics
Issue number23
StatePublished - 21 Jun 2019


FundersFunder number
Office of Basic Energy Sciences
U.S. Department of Energy
Division of Materials Sciences and EngineeringDEAC02-05-CH11231


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