Exact stochastic mean-field approach to the fermionic many-body problem

Area of Science:

• Quantum mechanics
• Many-body physics
• Computational physics

Background:

• Interacting fermion systems are fundamental in many areas of physics.
• Accurate simulation of these systems is computationally challenging.
• Existing methods like time-dependent Hartree-Fock have limitations.

Purpose of the Study:

• To develop a new stochastic formulation for simulating interacting fermion systems.
• To provide an alternative to traditional methods for solving many-body problems.
• To analyze the stability and convergence of the proposed method.

Main Methods:

• Reformulation of dynamics using a stochastic extension of time-dependent Hartree-Fock equations.
• Utilizing a path-integral representation of the evolution operator.
• Employing imaginary time propagation for ground state convergence.

Main Results:

• The exact N-body state is shown to be a coherent average over Slater determinants in a random mean-field.
• The imaginary time propagation scheme converges to the exact ground state.
• Analysis of statistical error growth demonstrates the formulation's stability.

Conclusions:

• The stochastic extension of time-dependent Hartree-Fock provides a stable and accurate method for simulating interacting fermion systems.
• This approach offers a new perspective on solving complex many-body quantum problems.
• The method shows promise for future applications in condensed matter and nuclear physics.