We analyze the quantum phase diagram of the Holstein-Hubbard model using an asymptotically exact strong-coupling expansion. We find all sorts of interesting phases including a pair-density wave (PDW), a charge 4e (and even a charge 6e) superconductor, regimes of phase separation, and a variety of distinct charge-density-wave (CDW), spin-density-wave (SDW) and superconducting regimes. We chart the crossovers that occur as a function of the degree of retardation, i.e. the ratio of characteristic phonon frequency to the strength of interactions.
@article{arxiv.2006.16253,
title = {Strong Coupling Limit of the Holstein-Hubbard Model},
author = {Zhaoyu Han and Steven A. Kivelson and Hong Yao},
journal= {arXiv preprint arXiv:2006.16253},
year = {2020}
}