The one-dimensional Holstein model revisited

TL;DR

This paper revisits the phase diagram of the one-dimensional Holstein model at half-filling, using density-matrix renormalization group simulations to clarify the nature of phases and phase boundaries across different regimes.

Contribution

It provides a corrected and detailed analysis of the ground-state phases of the 1D Holstein model, especially in the anti-adiabatic and strong coupling regimes, using advanced numerical methods.

Findings

Identification of two distinct phases: charge-density-wave and Luther-Emery phase.

Correction of previous inferences about phase boundaries in certain regimes.

Phase boundary shape reflects different microscopic physics in weak and strong coupling limits.

Abstract

We analyze the global ground-state (quantum) phase diagram of the one-dimensional Holstein model at half-filling as a function of the strength of the electron-phonon coupling (represented by the strength of the phonon-induced attraction, $U$) and the phonon frequency, $\omega_0$. In addition to reanalyzing the various asymptotic regimes, we have carried out density-matrix renormalization group simulations to correct previous inferences concerning the anti-adiabatic (large $\omega_0$) and strong coupling (large $U$) regimes. There are two distinct phases - a fully gapped commensurate charge-density-wave and a spin-gapped Luther-Emery phase with a gapless charge mode - separated by a phase boundary, with a shape that reflects different microscopic physics in the weak and strong coupling limits.