Stochastic nodal surfaces in quantum Monte Carlo calculations

Area of Science:

• Quantum physics
• Computational chemistry
• Many-body problem

Background:

• Fermionic systems present significant computational challenges for determining ground states.
• Existing quantum Monte Carlo methods often rely on trial wave functions, which can introduce biases.

Purpose of the Study:

• To develop a novel quantum Monte Carlo formalism for fermionic systems.
• To eliminate the requirement for trial wave functions in calculations.
• To improve the stability and efficiency of determining fermionic ground states.

Main Methods:

• The study frames the fermionic ground state problem as a constrained stochastic optimization problem.
• Exchange symmetry is enforced using nonlocal terms in the Green's function.
• A diffusion treatment is incorporated to promote the formation of a stochastic nodal surface.
• An approximate long-range extension of walker cancellations is employed to mitigate bias.

Main Results:

• The developed formalism successfully determines fermionic ground states without trial wave functions.
• The method demonstrates stability for simple harmonic and atomic systems.
• The approach reduces the number of walkers needed for stable calculations.
• Bias introduced by walker cancellations is shown to be insignificant.

Conclusions:

• The new quantum Monte Carlo formalism offers a robust and efficient alternative for fermionic ground state calculations.
• This method advances computational approaches to quantum many-body problems.
• The findings pave the way for more accurate simulations of complex fermionic systems.