Computation of the High Temperature Coulomb Density Matrix in Periodic Boundary Conditions

TL;DR

This paper introduces a new method for accurately computing the high temperature Coulomb density matrix in periodic systems, improving the precision of path integral simulations involving Coulomb interactions.

Contribution

A novel approach for consistent high-accuracy treatment of Coulomb interactions in periodic boundary conditions within path integral methods.

Findings

More accurate high temperature solutions of the Bloch equation.

Validated method on hydrogen atom and molecule.

Enhanced simulation accuracy for many-body systems.

Abstract

The high temperature many-body density matrix is fundamental to path integral computation. The pair approximation, where the interaction part is written as a product of pair density matrices, is commonly used and is accurate to order tau squared, where tau is the step size in the imaginary time. Here we present a method for systems with Coulomb interactions in periodic boundary conditions that consistently treats the all interactions with the same level of accuracy. It shown that this leads to a more accurate high temperature solution of the Bloch equation. The method is applied to many-body simulation and tests for the isolated hydrogen atom and molecule are presented.