Action-Based Quantum Monte Carlo Approach to Fermion-Boson Lattice Models

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Using the quantum Monte Carlo method, this project aims at understanding fundamental effects in models describing the interaction of fermionic charge carriers (electrons, holes) with bosonic degrees of freedom (phonons, magnons). The models of interest here capture electronic correlations and quantum fluctuations, and pose a challenge even to state of the art numerical methods. Despite some necessary simplifications, there are close connections to real compounds studied in experiments. Important aspects to be addressed include the Peierls transition from a metallic to an insulating state, the formation of polaronic charge carriers, the competition between charge density wave order and superconductivity, soliton excitations in polymers, and the role of spin fluctuations for electronic pairing. At the heart of this work will be the powerful continuous-time quantum Monte Carlo method, whose general action-based formulation allows us to study a great variety of physical problems.