On the Chemical Potential of Many-Body Perturbation Theory in Extended Systems

Finite-temperature many-body perturbation theory in the grand-canonical ensemble is fundamental to numerous methods for computing electronic properties at nonzero temperature, such as finite temperature coupled-cluster. In most applications it is the average number of electrons that is known rather than the chemical potential. Expensive correlation calculations must be repeated iteratively in search for the interacting chemical potential that yields the desired average number of electrons. In extended systems with mobile charges the situation is particular, however. Long-ranged electrostatic forces drive the charges such that the average ratio of negative and positive charges is one for any finite chemical potential. All properties per electron are expected to be virtually independent of the chemical potential, as they are in an electric wire at different voltage potentials. This work shows that per electron, the exchange-correlation free energy and the exchange-correlation grand potential indeed agree in the infinite-size limit. Thus, only one expensive correlation calculation suffices for each system size, sparing the search for the interacting chemical potential. This work also demonstrates the importance of regularizing the Coulomb interaction such that each electron on average interacts only with as many electrons as there are electrons in the simulation, avoiding interactions with periodic images. Numerical calculations of the warm uniform electron gas have been conducted with the Spencer-Alavi regularization employing the finite-temperature Hartree approximation for the self-consistent field and linearized finite-temperature direct-ring coupled-cluster doubles for treating correlation.