Worldline numerics: quantum field theory inspired numerical simulations of electron-hole pairs

We adapt a numerical technique originally arising out of the worldline approach to quantum field theory to study Coulomb interactions in condensed matter systems. The technique is based on the path integral formalism, using an ensemble of particle worldlines to probe the system, its energy spectrum and inter-particle interactions. Doing this requires us to generalise this numerical framework to multi-particle systems.
We apply the method to study the ground state energy of exciton-like systems and related scenarios involving three particles, incorporating externally applied fields alongside long-range Coulomb interactions. Finally, we will show more recent results applying the same, first quantised approach to study the creation of particle / anti-particle pairs due to fluctuations in a curved space-time.