Peierls instability and optical response in the one--dimensional half--filled Holstein model of spinless fermions

TL;DR

This paper investigates how quantum lattice fluctuations influence the Peierls transition in a one-dimensional Holstein model of spinless fermions, revealing phase diagram details and optical response differences.

Contribution

It provides a comprehensive phase diagram and optical spectra analysis using exact diagonalization and variational methods, aligning with recent DMRG results.

Findings

Transition to charge-density-wave regime marked by increased charge structure factor

Distinct optical absorption spectra characterize metallic and charge-density-wave phases

Finite-size scaling yields Luttinger liquid parameters in the metallic regime

Abstract

The effects of quantum lattice fluctuations on the Peierls transition are studied within the one--dimensional Holstein molecular crystal model by means of exact diagonalization methods. Applying a very efficient variational Lanczos technique, the ground--state phase diagram is obtained in excellent agreement with predictions of recent density matrix renormalization group calculations. The transition to the charge--density--wave regime is signaled by a strong increase in the charge structure factor. In the metallic regime, the non--universal Luttinger liquid parameters (charge velocity and coupling constant) are deduced from a finite--size scaling analysis. The variational results are supported by a complete numerical solution of the quantum phonon Holstein model on small clusters, which is based on a well--controlled phonon Hilbert space truncation procedure. The metallic and charge--density--wave phases are characterized by significant differences in the calculated optical absorption spectra.