Charge density waves on a half-filled decorated honeycomb lattice
Chunhan Feng, Huaiming Guo, Richard T. Scalettar
Abstract
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 ${t}^{\ensuremath{'}}$. 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 $t/{t}^{\ensuremath{'}}$ values which support a charge density wave phase about the Dirac point of uniform hopping $t={t}^{\ensuremath{'}}$, as well as the critical transition temperature ${T}_{c}$. The QMC simulations are compared with the results of mean field theory.