Mott-Insulator to Peierls Insulator Transition in the Two-Dimensional Holstein-Hubbard Model

We propose a variational study of the two dimensional square lattice to study the phase transition from an antiferromagnetic SDW Mott insulator to the bipolaronic CDW Peierls insulator for the half-filled Holstein Hubbard model. The correlated system is dealt analytically in two different regimes according to the renormalized Coulomb correlation strength. Different unitary transformations are performed to obtain an effective electronic Hamiltonian which is solved by using the mean-field Hartree-Fock approximation for the weakly correlated electrons. For the strong interaction case, the Zuberev's Green function technique is used to solve the effective t - J model at the mean field limit. The variations of the effective Hubbard hopping parameter and the effective Coulomb interaction strength for different electron-electron and electron-phonon interaction coefficients have been studied. We have found a transition from the Mott-insulator to a Peierls insulator analytically for the two dimensional Holstein Hubbard model. Copyright (C) 2022 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the Condensed Matter Physics.