Spectral density method applied to the study of the energy spectrum of the XY model in a transverse field

Abstract

The energy spectrum of the XY model in a transverse field is studied by the spectral density method (SDM), using polar and Gaussian "ansatze". Expressions for the critical temperature and critical transverse field are obtained. It is shown that, within some approximations, the static properties of this model are not modified by including damping effects in the elementary excitations.Unter Benutzung von polaren und Gad-,,AnsatZen" wird das Energiespektrum des XY-Modells in einem transversalen Feld mittels der Spektraldichtemethode (SDM) untersucht. Ausdriicke fur die kritische Temperatur und das kritische transversale Feld werden erhalten. Es wird gezeigt, daB, im Rahmen einiger Naherungen, die statischen Eigenschaften dieses Modells durch EinschluB von Dampfungseinfliissen in den Elementaranregungen ni?ht modifiziort werden.

The Moment Sum Rule and Its Consequences for Ferromagnetism in the Hubbard Model

“…(HF) −σ in (40). By construction the moments of the spectral density are correct up to m = 3 in the IAA.…”

“…This differs from the MAA self-energy with respect to the modified propagator; also T 0 is replaced by B HF Às in (40). By construction the moments of the spectral density are correct up to m 3 in the IAA.…”

“…We will argue that the first four moments (m = 0 − 3) yield valuable information on the quasiparticle band structure; they are especially important in the strong-coupling regime and also decisively influence the possibility and characteristics of spontaneous magnetic order. The moment sum rule has been considered not only within the context of the standard single-band Hubbard model in d = ∞ [22,23,24,25], in d = 3 [26,27,28,29,30], d = 2 [31,32,33] and d = 1 [31], but also for the negative-U case [34] and for reduced translational symmetry [35,36], for the SIAM [37], for the t-J [38] and for localized spin models [39,40,41] and may thus be of general interest for the construction of analytical approaches.…”

Magnetism in the single-band Hubbard model

“…The method is based on a physically motivated ansatz for the single-electron spectral density. The spectral density approach has proven to be very successful studying various many body problems such as Bose, Fermi and classical systems [26][27][28] . The main advantages of this method are the physically simple concept and the explicit non-perturbative character.…”

“…It turns out to be essentially equivalent to the Roth method 8,23 and to the Mori-projector formalism 24,25 . Various applications to Bose-, Fermi-, and classical systems [26][27][28] have proven the efficiency of the SDA. Previous applications of the SDA to the problem of band magnetism in the Hubbard model for the bulk 22 as well as for systems with reduced symmetry 29 have been restricted to a local selfenergy that could be derived self-consistently.…”