* Corresponding author. Tel.: #213-7-562909; fax: #213-7- 561486. E-mail address: haourag@mail.univ-sba.dz (H. Aourag). Physica B 301 (2001) 299 } 309 Quantum Monte Carlo study of the alternating extended Peierls}Hubbard model applied to the trans-polyacetylene S. Goumri-Said, H. Aourag*, F. de Fornel, L. Salomon Computational Materials Science Laboratory, Physics Department, University of Sidi Bel-Abbes, 22 Rue Hoche, Sidi Bel-Abbes 22000, Algeria LPUB, Optique de Champ Proche, Universite & de Bourgogne, Dijon, France Received 16 September 2000 Abstract The one-dimensional alternating Peierls}Hubbard model is especially interesting as nontrivial model for conjugated polymer chains, such as polyacetylene. We study this model for chains of 64 sites using the determinantal method based on Hubbard}Stratonovich transformation. We obtain the "rst electronic energies and their mean #uctuations at half-"lling as a function of the on-site electron}electron interaction (both short and long range ;, < coupling are considered). We also study the e!ect of the electron}electron interaction on the dimerization by investigating some of the important correlation functions, such as spin}spin correlation, on-site charge and the speci"cheat.Thee!ect of nonlinear excitations is also examined, particularly soliton excitation.  2001 Elsevier Science B.V. All rights reserved. Keywords: Peierls}Hubbard model; Electron}electron interaction; Electron}phonon interaction; Correlation functions; Trans-poly- acetylene, Quantum Monte Carlo simulation 1. Introduction The characteristic of that, the -conjugated poly- mers lie at the interface between organic chemistry and solid-state physics have generated substantial interest in both disciplines. Known as good insula- tors, design and synthesis of polymers has resulted new materials that bring a vast range of application in electronic products in sight. Bare codes, poly- mers light-emitting diodes (PLEDs) and polymer solar cells constitute a fascinating "eld of research which has attracted special attention of physicists. Also, the low production cost is the most feature of these materials, which has enhanced their tech- niques of synthesis and more generally the experi- mental research [1}3]. In theoretical "elds, for the past years, there has been enormous research in the properties of poly- mer, and more specially conducting polymers. As a consequence, a wide range of the theoretical mod- els and even a panoply of calculational methods have been applied to the study of these materials and the most important related phenomena. Con- jugated polymers are viewed as a member of class of quasi-one dimensional system, which possess the broken-symmetry ground-state as common feature. 0921-4526/01/$-see front matter  2001 Elsevier Science B.V. All rights reserved. PII:S0921-4526(01)00278-2