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

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The interaction between fermionic and bosonic degrees of freedom plays animportant role in many areas of condensed matter physics. A key example isthe coupling of electrons to lattice vibrations (phonons) in a solid, whichunderlies phenomena such as superconductivity or the Peierls instability.In this project, we will apply exact numerical methods to improve ourunderstanding of different fermion-boson models. We will, for example,investigate the role of an unscreened electron-phonon interaction forsuperconductivity, or the effect of phonons on the temperature dependence ofthe specific heat and heat transport. Moreover, we will study the crossoverfrom one-dimensional chains, which are dominated by the Peierls instability,to two dimensions. Finally, we will investigate a recently proposed model forhigh-temperature superconductivity mediated by spin fluctuations.The unbound number of bosonic excitations, and the different time scales ofthe fermion and boson dynamics pose a challenge even for modern numericalmethods. We will use a continuous-time quantum Monte Carlo method that isparticularly suited to investigate complex fermion-boson problems. Thebosonic degrees of freedom can be integrated out to obtain a purely fermionicproblem that can be simulated very efficiently, and without systematicerrors.Our results are expected to be relevant for low-dimensional materials such aspolymers, dichalcogenides, or cuprate superconductors. Moreover, themethodological developments are expected to enable investigations of othercomplex fermion-boson problems in the future.