Action-based quantum Monte Carlo approach to fermion-boson lattice models

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By extending the continuous-time quantum Monte Carlo method, this project aims at understanding fundamental effects in models describing the interaction of fermionic charge carriers with bosonic degrees of freedom such as phonons or magnons. The models of interest here capture electronic correlations and quantum fluctuations, and pose a challenge even to state of the art numerical methods. The action-based path-integral formulation of the continuous-time quantum Monte Carlo method permits to include general, nonlocal two-particle interactions mediated by bosons. Important aspects to be addressed include the Peierls transition, polaron formation, the competition between charge-density-wave order and superconductivity, soliton excitations in polymers, and the role of spin fluctuations for electronic pairing.