A new version of fermion coupled coherent states method: Theory and applications in simulation of two-electron systems

TL;DR

The paper introduces an improved fermion coupled coherent states method (FCCS-II) that simplifies symmetrization, enhances computational efficiency, and enables accurate simulation of two-electron quantum systems like helium and hydrogen molecules.

Contribution

FCCS-II simplifies the symmetrization process, increases computational speed, and extends the applicability of fermion coupled coherent states methods to larger quantum systems.

Findings

FCCS-II accurately simulates potential energy curves for H2.

FCCS-II achieves faster computations with larger coherent state grids.

The method reproduces key equations of FCCS-I, confirming its validity.

Abstract

We report a new version of fermion coupled coherent states method (FCCS-II) to simulate two-electron systems based on a self-symmetrized six-dimensional (6D) coherent states grid. Unlike the older fermion coupled coherent states method (FCCS-I), FCCS-II does not need any new equations in comparison with the coupled coherent states method. FCCS-II uses a simpler and more efficient approach for symmetrizing the spatial wave function in the simulation of fermionic systems. This method, has significantly increased the speed of computations and give us the capability to simulate the quantum systems with the larger CS grids. We apply FCCS-II to simulate the Helium atom and the Hydrogen molecule based on grids with a large numbers of coherent states. FCCS-II with a relatively low number of CS gives a potential energy curve for H2 that is very close to the exact potential curve. Moreover, we have re-derived all the important equations of the FCCS-I method.