KelbgLIP: Program implementation of the high-temperature Kelbg density matrix for path integral and molecular dynamics simulations with long-range Coulomb interaction

In this paper, we present the KelbgLIP code to implement the previously obtained analytical density matrix that includes Coulomb long-range interactions. The method is based on the work of G. Kelbg, who derived a high temperature density matrix for the Coulomb potential. To include all long-range interactions in the density matrix, we use the Ewald technique, specifically the angular-averaged Ewald potential (AAEP). The solution of the Blöch equation within the AAEP has a direct analytic form that can be easily implemented in classical and quantum Monte Carlo or molecular dynamics codes, including exchange effects. The potential part of the density matrix remains finite at small distances, preventing the collapse of a two-component system. Using KelbgLIP, one can calculate the diagonal Kelbg-AAE pseudopotential and the pair density matrix. In the case of a hydrogen plasma, the code is able to calculate action, kinetic and potential energy in the path integral representation. We validated our approach by simulating a nondegenerate weakly coupled hydrogen plasma and obtained the thermodynamic limit in agreement with the Debye-Hückel approximation. In addition, we observe the agreement with classical simulations using the unbounded from below AAEP, which is possible in the weakly-coupled regime.