Metal-insulator transition in the one-dimensional Holstein model at half filling

TL;DR

This paper investigates the metal-insulator transition in the one-dimensional Holstein model at half-filling, revealing how quantum lattice fluctuations influence the ground state and phase transitions.

Contribution

It provides highly accurate numerical analysis of the phase diagram, demonstrating the destruction of the Peierls insulator by quantum fluctuations and characterizing the transition to an insulating phase.

Findings

Quantum lattice fluctuations destroy the Peierls insulator at small coupling.

Transition to a Peierls insulator occurs at large coupling or low phonon frequency.

The insulating phase exhibits long-range charge order and a spectral gap.

Abstract

We study the one-dimensional Holstein model with spin-1/2 electrons at half-filling. Ground state properties are calculated for long chains with great accuracy using the density matrix renormalization group method and extrapolated to the thermodynamic limit. We show that for small electron-phonon coupling or large phonon frequency, the insulating Peierls ground state predicted by mean-field theory is destroyed by quantum lattice fluctuations and that the system remains in a metallic phase with a non-degenerate ground state and power-law electronic and phononic correlations. When the electron-phonon coupling becomes large or the phonon frequency small, the system undergoes a transition to an insulating Peierls phase with a two-fold degenerate ground state, long-range charge-density-wave order, a dimerized lattice structure, and a gap in the electronic excitation spectrum.