Charge Density Waves on a Half-Filled Decorated Honeycomb Lattice

TL;DR

This study investigates charge density wave formation on a decorated honeycomb lattice with non-uniform hopping, using quantum Monte Carlo simulations to analyze phase stability and transition temperatures in the presence of electron-phonon interactions.

Contribution

It provides the first detailed quantum Monte Carlo analysis of the Holstein model on a decorated honeycomb lattice with non-uniform hopping, revealing conditions for charge density wave phases.

Findings

Charge density wave phase exists for certain hopping ratios.

Transition temperature T_c depends on hopping modulation.

Quantum Monte Carlo results are consistent with mean field theory.

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 non-uniform $t$ has been studied within a number of situations, perhaps most prominently in multi-band 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 $t^{\,\prime}$. 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 $t/t^{\,\prime}$ values which support a charge density wave (CDW) phase about the Dirac point of uniform hopping $t=t^{\,\prime}$, as well as the critical transition temperature $T_c$. The QMC simulations are compared with the results of Mean Field Theory (MFT).