We study the Coulomb-Frohlich model on a triangular lattice, looking in particular at states with angular momentum. We examine a simplified model of crab bipolarons with angular momentum by projecting onto the low energy subspace of the Coulomb-Frohl
ich model with large phonon frequency. Such a projection is consistent with large long-range electron-phonon coupling and large repulsive Hubbard $U$. Significant differences are found between the band structure of singlet and triplet states: The triplet state (which has a flat band) is found to be significantly heavier than the singlet state (which has mass similar to the polaron). We test whether the heavier triplet states persist to lower electron-phonon coupling using continuous time quantum Monte Carlo (QMC) simulation. The triplet state is both heavier and larger, demonstrating that the heavier mass is due to quantum interference effects on the motion. We also find that retardation effects reduce the differences between singlet and triplet states, since they reintroduce second order terms in the hopping into the inverse effective mass.
We consider the effects of single impurities on polarons in three-dimensions (3D) using a continuous time quantum Monte-Carlo algorithm. An exact treatment of the phonon degrees of freedom leads to a very efficient algorithm and we are able to comput
e the polaron dynamics on an infinite lattice using an auxiliary weighting scheme. The magnitude of the impurity potential, the electron-phonon coupling and the phonon frequency are varied. We determine the magnitude of the impurity potential required for polaron trapping. For small electron-phonon coupling the number of phonons increases dramatically on trapping. The polaron binding diagram is computed, showing that intermediate-coupling low-phonon-frequency polarons are localized by exceptionally small impurities.
