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

Martin Hohenadler, Fakher Assaad


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