Metal-insulator transition of spinless fermions coupled to dispersive optical bosons

TL;DR

This study investigates how phonon dispersion affects the metal-insulator transition in a one-dimensional spinless fermion system, revealing that phonon curvature significantly influences phase transitions and can induce phase separation.

Contribution

It introduces a modified spinless fermion Holstein model with dispersive phonons and uses matrix-product-state techniques to map the ground-state phase diagram, highlighting the impact of phonon dispersion.

Findings

Convex phonon dispersion shifts the transition to stronger coupling.

Concave phonon dispersion induces a phase-separated state.

Phase separation is absent in the Edwards fermion-boson model.

Abstract

Including the previously ignored dispersion of phonons we revisit the metal-insulator transition problem in one-dimensional electron-phonon systems on the basis of a modified spinless fermion Holstein model. Using matrix-product-state techniques we determine the global ground-state phase diagram in the thermodynamic limit for the half-filled band case, and show that in particular the curvature of the bare phonon band has a significant effect, not only on the transport properties characterized by the conductance and the Luttinger liquid parameter, but also on the phase space structure of the model as a whole. While a downward curved (convex) dispersion of the phonons only shifts the Tomonaga-Luttinger-liquid to charge-density-wave quantum phase transition towards stronger EP coupling, an upward curved (concave) phonon band leads to a new phase-separated state which, in the case of strong dispersion, can even completely cover the charge-density wave. Such phase separation does not occur in the related Edwards fermion-boson model.