Computing Phonon Dispersion using Fast Zero-Point Correlations of Conjugate Variables

Time correlations of dynamic variables in the reciprocal space offer a rich theoretical setting for computing the phonon dispersion curves, particularly for systems with marked anharmonic interactions. Present techniques primarily rely either on the equipartition of energy between the phonon modes or on the oscillation of the time correlation of the normal mode projections. The former can lead to numerical errors due to deviation from equipartition while the latter usually requires long simulations for computing the time correlations. We investigate a different approach using the ratio of the normal mode expectation value of two conjugate variables - velocity and acceleration. Since only the correlations at the initial time (t=0) are needed, this approach is computationally attractive. In this work, we employ this method to extract the full Brillouin zone phonon dispersion for graphene.