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We study the quantum many-body ground states of electrons on the half-filledhoneycomb lattice with short- and long-ranged density-density interactions as amodel for graphene. To this end, we employ the recently developedtruncated-unity functional renormalization group (TU-fRG) approach which allowsfor a high resolution of the interaction vertex' wavevector dependence. Weconnect to previous lattice quantum Monte Carlo (QMC) results which predict astabilization of the semimetallic phase for realistic \emph{ab initio}interaction parameters and confirm that the application of a finite biaxialstrain can induce a quantum phase transition towards an ordered ground state.In contrast to lattice QMC simulations, the TU-fRG is not limited in the choiceof tight-binding and interaction parameters to avoid the occurrence of a signproblem. Therefore, we also investigate a range of parameters relevant to therealistic graphene material which are not accessible by numerically exactmethods. Although a plethora of charge density waves arise under medium-rangeinteractions, we find the antiferromagnetic spin-density wave to be theprevailing instability for long-range interactions. We further explore theimpact of an extended tight-binding Hamiltonian with second-nearest neighborhopping and a finite chemical potential for a more accurate description of theband structure of graphene's $p_z$ electrons.

Antiferromagnetism and competing charge instabilities of electrons in strained graphene from Coulomb interactions