In this work we report on two different strategies to deal with the fermion sign problem in context of Hybrid-Monte-Carlo simulations on the hexagonal graphene lattice. The first approach is to simulate a theory, which have no sign problem, by taking advantage of the particle-hole symmetry of the band structure of graphene and applying a spin dependent chemical potential which is in the non interacting case equal to charge carrier density. There we take a realistic screened Coulomb potential into account and investigate the in uence of it on the band structure. In particular, we focus on the deviation on the band structure and the behavior of topological Lifshitz transition taking place at the van Hove singularity. Within this part we find evidence that the bandwidth is reduced by many-body interactions, which is in-line with experimental observations from angle resolved photoemission spectroscopy. Furthermore, our results indicate that the Lifshitz transition tend to become a true quantum phase transition in presence of interactions. In the second approach, we are dealing with an charge carrier chemical potential directly. Here, we use the Linear-Logarithmic-Relaxation method to compute a generalized density of states and use this as an input for a reconstruction of the particle density. We compare this approach with pure brute-force reweighting and show that the relative advantage of the method grows with increasing interaction strength. For the sake of simplicity we use the Hubbard model with only on-site interactions in this case. Finally, we discuss both variants and give an overview of possible further investigations or thinkable improvements of the methods.
Verknüpfung zu Publikationen oder weiteren Datensätzen
