Influence of Thermal Fluctuations of Spin Density Wave Order Parameter on the Quasiparticle Spectral Function. M. Khodas and A.M. Tsvelik Department of Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, NY 11973-5000, USA The two-dimensional model of itinerant electrons coupled to an anti-ferromagnetic order parame- ter is considered. In the mean field solution the Fermi surface undergoes reconstruction, and breaks into disconnected “pockets”. We have studied the effect of the thermal fluctuations of the order parameter on the spectral density in such system. These fluctuations lead to a finite width of the spectral line scaling linearly with temperature. Due to the thermal fluctuations the quasi-particle spectral weight is transfered into a magnetic Brillouin zone. This can be interpreted as restoration of “arcs” of the non-interacting Fermi surface. PACS numbers: 71.27.+a, 75.30.Fv, 71.10.-w I. INTRODUCTION Fluctuations play a prominent role in systems of re- duced dimensionalities leading to a complete or partial suppression of long range order and rendering mean field approximation inapplicable. Calculation of correlation functions then becomes an arduous task. The question is whether in the absence of true long range order these functions display features of the ordered state and if yes, to what extent. The correlation function we are con- cerned with in this paper is the single electron spec- tral function. Measurements of this function constitute the most powerful experimental probes in the physics of strongly correlated systems. We discuss the situation when the system is close to being antiferromagnetically ordered and study the effect of thermal order parameter fluctuations. There is a considerable literature addressing the influ- ence of quantum fluctuations (we refer the reader to [1] and [2] which also provide references to the related pa- pers). However, at finite temperatures one has to take into account thermal fluctuations which brings specific problems. In our previous publication [3] we consid- ered the influence of thermal fluctuations on the spectral function of a two dimensional (2D) superconductor. 2D superconductors have quasi long range order such that phase fluctuations are critical in the entire temperature region below T$_{c}$ . We have found that at least as far as the thermal fluctuations were concerned, the frequently used approach based on the conversion of this problem into a gauge theory turned out to be inadequate. The latter approach includes a gauge transformation of the fermion fields with a subsequent attempts to treat the problem as a gauge field theory one (as, for instance, in [2]). The difficulty comes from the fact that the re- sulting calculational scheme contains strong ultraviolet divergencies and hence requires knowledge about states located far from the Fermi surface. As an alternative we have suggested the direct perturbation expansion in the order parameter. This procedure contains only infrared divergencies and is therefore universal. with the index i enumerating two subbands related by the vector Q . The sum in Eq. (2) is over small mo- menta and two subbands can be combined together (see where k is a momentum vector in the Brillouin zone, and α is the spin index. The kinetic energy close to the ”hot spots” can be approximated as We consider a popular spin-fermion model in two- dimensions where electrons interact with a commensu- rate SDW [1]. The antiferromagnetic ordering open gaps at the points of the Fermi surface (FS) connected by the vector of anti-ferromagnetic fluctuation Q = ( π, π ), see Fig. 1. As a result the FS undergoes reconstruction into disconnected pockets. The Hamiltonian for quasiparti- cles located near two FS points connected by Q is In the present paper we apply the approach of [3] to cal- culate the spectral function in the presence of a fluctuat- ing commensurate Spin Density Wave (SDW). This prob- lem has a potential relevance to the problem of cuprates. There is a significant experimental evidence in favor of Fermi surface reconstruction taking place in the under- doped phase of the copper oxide superconductors (see, for example, [4],[5]). On the other hand, it is still un- clear whether one needs a real long range order to observe such reconstruction or a short range one will suffice. In the present paper we will address this question in the context of the spectral function. We consider only clas- sical (thermal) fluctuations of the order parameter. This is more than an academic excercise since thermally fluc- tuating SDW phase has been suggested to occupy a part of the cuprate phase diagram in the strongly underdoped regime [6]. II. DESCRIPTION OF THE MODEL AND THE RESULTS. H = ∑ k α ξ ( k ) ψ † k $_{α}$ψ$_{k}$$_{α}$ + J ∑ k S ψ † k + Q $_{α}$σ$_{αβ}$ ψ$_{k}$$_{β}$ , (1) ∑ k α ξ ( k ) ψ † k $_{α}$ψ$_{k}$$_{α}$ ≈ ∑ i =1 , 2 ∑ k α v$_{i}$k ψ † i k $_{α}$ψ$_{i}$$_{k}$$_{α}$ (2) arXiv:1001.0590v1 [cond-mat.str-el] 4 Jan 2010