Computation of the high temperature Coulomb density matrix in periodic boundary conditions

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 τ2τ2, where ττ 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 is 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.