Rachel Emrick Research Project

Rachel Emrick (UNC Math/CS/Physics undergrad)

Project: Efficient calculation of matrix exponentials using decomposition.

Abstract: The matrix exponential exp(-beta H) is an important quantity for quantum thermodynamics, but it can be very difficult or impossible to calculate directly. Using operator splitting (H = T + V, where T is diagonal and V is low-rank), Suzuki-Trotter decompositions have been developed which use the basis of exp(-T) and exp(-V) to approximate exp(-beta H). Using numerical experiments, we explore the two-body problem in three dimensions to try to discover regimes for which certain decompositions are preferable. We consider changing step size as well as changing the strength of particle interactions to examine various decompositions.

In the future, we hope to compare the results from this project with the results from another group exploring decompositions which use a polynomial basis. Our results will also be relevant to the computational quantum matter group who are building the quantum thermodynamics computational engine (see https://tarheels.live/qtce/) and hopefully other simulators that may use these numerical methods in general.