One Dimensional Acoustic Phonon Linearly Coupled to Electron Density (Bulletin of Pure and Applied Sciences – Physics, 2020)
We have studied one dimensional acoustic phonon linearly coupled to the electron  density. The phonon spectrum is linear with cutoff at the Debye frequency, it is  straightforward modification of three dimensional optical phonons. Phonon field  results in substituting the dynamical coupling for the screened coulomb interaction.  We have shown that the electron-phonon coupling quantitatively changed the phase  diagram of Luttinger liquid with a single impurity. The existence of slow and fast  polaron modes with different weights in different regimes resulted in different  renormalization group flow for a weak scatterer and a weak tunneling link. The  resulting phase diagram depending on the parameters of the problem, regimes  corresponding to purely metallic or purely insulating behavior and an intermediate  regime with two stable fixed points and one unstable, finite conductance fixed point.  we have found that the direction of renormalization group flow change upon  varying either the relative strength of the electron-electron and electron-phonon  coupling or the ratio of Fermi to sound velocities. The obtained results were found in  good agreement with previously obtained results.