Solid State Sciences 4 (2002) 757–765 www.elsevier.com/locate/ssscie The behavior of correlation functions in trans-polyacetylene: quantum Monte Carlo study S. Goumri-Said a,b , H. Aourag a , L. Salomon b,∗ , J.-P. Dufour b a Computational Materials Science Laboratory, Physics Department, University of Sidi Bel-Abbes, 22 rue Hoche, Sidi Bel-Abbes 22000, Algeria b Laboratoire de Physique (LPUB), CNRS UMR 5027, Université de Bourgogne, Groupe d’Optique de Champ Proche, Faculté des Sciences Mirande, 9, avenue Alain Savary, BP 47 870-21078 Dijon cedex, France Received 24 September 2001; received in revised form 15 March 2002; accepted 19 March 2002 Abstract We present results of a quantum Monte Carlo simulation of the one-dimensional half-filled Hubbard model to study different correlation functions in the trans-polyacetylene (t-PA) polymer. Magnetic structure of the model in t-PA is studied for a different range values of the Hubbard repulsion interactions, U and V , where U< 4t , U ≈ 4t and U> 4t , with V ∈[U/2,U ] (t is the hopping matrix elements). In this work, we investigate the behavior of the magnetic correlation functions for different phases transitions between different ordering (antiferromagnetic and ferromagnetic) by varying the nearest-neighbor interactions U and V between different atomic sites. Our results indicate that there is a presence of a substantial delocalization of the electrons for a specified sets of correlation parameters. This feature, represented by the magnetic local moment observable reflects the influence of both (U,V) and quantum fluctuations. The behavior of the magnetic susceptibility is confirmed and interpreted by the calculation of the specific heat versus the inverse temperature for different mentioned regimes.  2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Keywords: Correlation functions; Hubbard model; Quantum Monte Carlo simulation; Trans-polyacetylene 1. Introduction One-dimensional or more generally low-dimensional ma- ny-body systems are a fascinating field of research not only because of their mathematical tractability, but also, because of the underlying physics is different from that of the higher- dimensional systems. Among these systems which have attracted more attention of both physicists and chemists, are polymers [1]. The problem of finding an accurate physical description of the quasi-one-dimensional organic polymers has a long history [2–4]. One of the origin of the difficulty is the ex- istence of different kinds of models [5–8] (both in quantum chemistry and in solid state physics) which can be applied to these systems. Theoretical investigations of these systems are gener- ally exceedingly difficult owing to the many-body nature of the problem. For this task, many theories have been de- * Correspondence and reprints. E-mail addresses: sgoumri@u-bourgogne.fr (S. Goumri-Said), lsalomon@u-bourgogne.fr (L. Salomon). veloped to deal with the different interactions: electron– electron (e–e) and electron–phonon (e–ph) interactions and the physics of the different elementary excitations (soliton, polaron, bipolaron, etc.) [6]. The debate between single- electron approaches and many-body theories has been long standing. If we consider the case of polyacetylene –(CH) x – classified as a quasi-one-dimensional conjugated polymer, the soliton theory [7–11] has achieved an understanding of many properties, such as electronic, optical, magnetic and transport properties of polymers [5,6]. In the early version of this theory, only electron–lattice coupling was taken into account whereas electrons interaction were neglected. How- ever, many experiments demonstrated the importance of the e–e interaction, for example, in the optical absorption associ- ated with neutral soliton [12] and the non vanishing negative spin density on the alternate carbon atoms [13]. Many methods have been developed to investigate the electrons interaction. Among them: the mean field and per- turbation methods [14], the valence–bond method [15–18], the renormalized-group method [19], Monte Carlo simula- tion [20]. 1293-2558/02/$ – see front matter  2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. PII:S1293-2558(02)01337-7