Charge density waves on a half-filled decorated honeycomb lattice

Tight binding models like the Hubbard Hamiltonian are most often explored in the context of uniform intersite hopping t. The electron-electron interactions, if sufficiently large compared to this translationally invariant t, can give rise to ordered magnetic phases and Mott insulator transitions, especially at commensurate filling. The more complex situation of nonuniform t has been studied within a number of situations, perhaps most prominently in multiband geometries where there is a natural distinction of hopping between orbitals of different degree of overlap. In this paper we explore related questions arising from the interplay of multiple kinetic energy scales and electron-phonon interactions. Specifically, we use determinant quantum Monte Carlo (DQMC) to solve the half-filled Holstein Hamiltonian on a "decorated honeycomb lattice," consisting of hexagons with internal hopping t coupled together by t′. This modulation of the hopping introduces a gap in the Dirac spectrum and affects the nature of the topological phases. We determine the range of t/t′ values which support a charge density wave phase about the Dirac point of uniform hopping t=t′, as well as the critical transition temperature Tc. The QMC simulations are compared with the results of mean field theory.