Anharmonic Peierls model in the low electronic density limit

The Peierls model of electron-phonon coupling is usually derived assuming small displacements of the atomic orbitals from their equilibrium configuration. In this case, the nearest-neighbor electronic hopping is modified at first order by a term which is linear in the phononic displacements. What happens if we relax this assumption? The inclusion of anharmonic terms is indeed expected to be important for large phononic displacements and large electron-phonon couplings.
In a recent study [arXiv:2008.03304 (2020)], we have shown that in the one dimensional linear Peierls model in the dilute electronic density limit an unusual phase separation regime breaking the 2k_F rule arises in a wide range of phononic frequencies and at large electron-phonon coupling strengths. In this talk, we will show (numerically, using DMRG) how such phase separated state is affected by the inclusion of anharmonic terms in the electron-phonon interaction as well as in the phononic potential energy at the Hamiltonian level. Finally, we will discuss the results in relation to high critical temperature superconductivity induced by electron-phonon coupling in realistic materials.