Long-Range Charge Order in the Extended Holstein–Hubbard Model

This study investigated the extended Holstein–Hubbard model at half-filling as a model for describing the interplay of electron–electron and electron–phonon couplings. When the electron–phonon and nearest-neighbor electron–electron interactions are strong, we prove the existence of long-range charge order in three or more dimensions at a sufficiently low temperature. As a result, we rigorously justify the phase competition between the antiferromagnetism and charge orders.