Stochastic Coherent State Path Integral approach to Electrons in a Solid

We develop a stochastic coherent state path integral approach for modeling finite-temperature systems. This is constructed so we can directly sample both Fermion and Boson operator eigenvalues, from any second quantised Hamiltonian. Standard path integral Monte Carlo techniques, sample eigenvalues of coordinate space operators, making the inclusion of spin physics challenging. In the case of the polaron problem this allows us to study more physical interaction forms, e.g. tight-binding models or quartic electron-phonon coupling. We use a spherical Gaussian basis expansion on a lattice. Further we compare to the closed-form solution of a non-interacting quantum harmonic oscillator with a two-site tight binding model, and find passable agreement. We then construct model Hamiltonians for polarons, and compare to ion-trapping experimental data. As we can simultaneously simulate an interacting hole and electron polaron, we predict exciton energies and lifetimes. These we compare to spectroscopic measurements of K-40 impure Bose-Einstein condensates, and solid state gallium nitride time-resolved photoluminesence. Surprisingly we find that electron-phonon coupling has only a moderate effects (10% ~ 40%) on electron-hole recombination times at physical ranges of system parameters. Temperature and, especially, the underlying electronic structure are determined to have the strongest effect on recombination rate. Our method is in early stages in applicability and validity, we believe this new method, could be useful when wanting to include spin-physics in Path-Integral Monte Carlo.