Phase transition and phase diagram at a general filling in the spinless one-dimensional Holstein Model

Abstract

Among the mechanisms for lattice structural deformation, the electron-phonon interaction mediated Peierls charge-density-wave (CDW) instability in single band low-dimensional systems is perhaps the most ubiquitous. The standard mean-field picture predicts that the CDW transition occurs at all fillings and all values of the electron-phonon coupling $g$ and the adiabaticity parameter $t/{\omega }_0$. Here, we correct the mean-field expression for the Peierls instability condition by showing that the non-interacting static susceptibility, at twice the Fermi momentum, should be replaced by the dynamic one. We derive the Luttinger liquid (LL) to CDW transition condition, {\it exact to second order in a novel blocked perturbative approach}, for the spinless one-dimensional Holstein model in the adiabatic regime. The small parameter is the ratio $g{\omega }_0/t$. We present the phase diagram at non-half-filling by obtaining the surprising result that the CDW occurs in a more restrictive region of a two parameter ($g^2{\omega }_0/t$ and $t/{\omega }_0$) space than at half-filling.

arXiv commentMade changes in the appendices and also in notation

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Cited by in corpus (4)

• The quantum vs classical aspects of one dimensional electron-phonon systems revisited by the renormalization group method
• Phase diagram of one-dimensional Hubbard-Holstein model at quarter-filling
• A study of cooperative breathing-mode in molecular chains
• Orbital ordering in undoped manganites via a generalized Peierls instability