Symmetrized projector quantum Monte Carlo studies of the ground state of C₆₀

Abstract

We develop a symmetrized version of the projector quantum Monte Carlo (SPQMC) method which preserves the symmetries of the system by simultaneously sampling all symmetry-related Ising configurations at each MC step and use it to study the effect of electron correlations on a single C₆₀ molecule and its structural motifs, within the Hubbard model. This SPQMC method allows more accurate estimates of correlation functions as seen from calculations on small systems. The method applied to some molecular fragments of C₆₀, viz., pyracylene, fluoranthene, and corannulene, gives a good chemical description of these systems. Analysis of the ground-state bond orders allows us to visualize pyracylene as a naphthalene moiety with weakly bridged ethylenic units, fluoranthene as weakly bridged naphthalene and benzene units, and corannulene as radialene with ethylenic bridges. We study the ground-state properties of a single fullerene molecule, with and without bond alternation. The bond orders in the ground state for the two types of nearest-neighbor bonds are unequal, even for uniform C₆₀. The spin and charge correlations give a consistent picture of the interacting ground state in all these systems. We construct projections of the bond orders and spin-spin correlation functions on the space of irreducible representations of the icosahedral point group. These projections, analogous to the structure factors of translationally invariant systems, give the amplitudes for distortions which transform as the irreducible representations of the point group. The amplitude for the H_g distortion is the largest, while the spin structure has large weights in the T_2g and G_u representations.