Phonons and Quantum Fluctuations in a Dimerized Electron-Phonon Chain

Abstract

The model Hamiltonian

$${\rm{H = }}\mathop \sum \limits_{\rm{j}} \left\{ {{\rm{ - }}\left[ {{\rm{t + a}}\left( {{{\rm{u}}_{\rm{j}}}{\rm{ - }}{{\rm{u}}_{{\rm{j + l}}}}} \right)} \right]{\mkern 1mu} ({{\rm{c}}_{{\rm{j + l ,\sigma }}}}{{\rm{c}}_{{\rm{j}},{\rm{\sigma }}}}{\rm{ + h}}{\rm{.c}}{\rm{.}}){\rm{ + }}\frac{{{{\rm{P}}_{\rm{j}}}^{\rm{2}}}}{{{\rm{2M}}}}{\rm{ + }}\frac{{\rm{D}}}{{\rm{2}}}{{\left( {{{\rm{u}}_{\rm{j}}}{\rm{ - }}{{\rm{u}}_{{\rm{j + l}}}}} \right)}^{\rm{2}}}} \right\}$$

(1)

was introduced by Su, Schrieffer and Heeger (SSH)¹ to describe electron-phonon interactions in polyacetylene.