Numerical Classical and Quantum Mechanical simulations of Charge Density wave models

TL;DR

This paper compares classical and quantum mechanical models for simulating Charge Density Waves, highlighting the importance of including Peierls condensation energy to accurately model soliton-based transport.

Contribution

It introduces a quantum simulation approach using the massive Schwinger model and demonstrates the necessity of Peierls energy for realistic CDW transport modeling.

Findings

Classical models exhibit unphysical blow-up at threshold fields.

Quantum models require Peierls energy for soliton tunneling.

Inclusion of Peierls energy enables realistic CDW transport simulation.

Abstract

We first present how to do a computer simulation of Charge Density Waves using a driven harmonic oscillator model by a numerical scheme as initially formulated by Littlewood, and then afterwards use this to present how the dielectric model as presented by this proceedure leads to a blow up at the initialization of a threshold field ET. We find that this is highly unphysical and this initiated our inquiry as to alternative models. Afterwards, we then investigate hwo to present this transport problem of CDW quantum mechanically, threough a numerical simulation of the massive Schwinger model. We find that this single chaing quantum mechanical simulation uwed to formulate solutions to CDW transport in itself is insufficient for transport of solitons(anti-solitons) through a pinning gap model of CDW. We show that a model Hamiltonian with Peierls condensation energy used to couple adjacent chains (or transverse wave vectors) permits formation of solitons (anti- solitons) which can be used to transport CDW through a potential barrier. This addition of the Peierls condensation energy term is essential for any quantum model of Charge Density Waves to give tunneling behavior as seen via a numerical simulation.