Transport properties of strongly correlated materials have contributions from quasiparticle excitations such as electrons and holes as well as emerging collective excitations such as plasmonic soundlike modes which are sustained by interactions. It was previously shown by Pongsangangan et al. [Phys. Rev. B 106, 205127 (2022)] that the thermal excitation of the long-lived plasmons in graphene provides a substantial contribution to heat and momentum transport in the interaction-dominated regime. Detailed information on these excitations is therefore necessary for the understanding of hydrodynamic transport with quantitative precision. On the other hand, dynamics of graphene plasmons is usually studied using perturbation theory within the Dirac cone approximation, thus neglecting the effects of a finite Brillouin zone (BZ) and higher-order perturbative corrections. Both these effects can be, however, significant for strong-interacting systems including free-standing graphene, where the effective coupling constant can reach values up to $\alpha =\frac{e^2}{\hslash v_{\mathrm{F}}}=2$. Consequently, in this paper, we study the behavior of plasmons in half-filled free-standing graphene using unbiased quantum Monte Carlo (QMC) calculations. We confirm the existence of well-defined resonance peaks for plasmons around the $\mathrm{\Gamma }$ point. Comparison with the random phase approximation (RPA) calculation for the honeycomb lattice shows qualitative agreement with QMC. However, RPA yields more stable plasmon modes, while QMC shows enhanced broadening due to nonperturbative interaction effects naturally included in the simulations. To account for this effect, we generalize the calculation of lattice RPA by dressing the fermionic propagator by a constant lifetime. As a result, the plasmon frequencies are shifted toward higher energies, and the spectrum is broadened, yielding better agreement with QMC. Our findings highlight the need to account for both a finite BZ and strong interaction effects when developing theories of electronic transport in free-standing graphene.

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• Plasmons
• Graphene
• Quantum Monte Carlo