New quantum Monte Carlo formulation for modeling trans-polyacetylene properties: specific heat calculation

Abstract

In this paper we propose a new hybridization scheme for numerical simulation based on the determinantal quantum Monte Carlo and analytical model to treat the vibration mode of one-dimensional trans -polyacetylene chain. We use both of the extended Hubbard model (EHM) and Peierls–Hubbard model to compute the specific heat for different assumptions. For both the two models, our results indicate that the behavior of the specific heat is characterized by a maximum. We also introduce the effect of dimerization through Peierls–Hubbard model. In this case it is found that the specific heat magnitude is slightly more important when compared to specific heat value found with the EHM case. Moreover the inclusion of electron–phonon interaction, the bond alternation and dimerization give an explication to the existence of quantum fluctuations, which may be associated to the existence of soliton solutions of the lattice vibration. The important result of this study is that the analytical ground state preserves size consistency and can be generalized for other geometries (e.g. cis -polyacetylene, polyacene, etc.), while still being both easy to interpret and to evaluate accurately.