Spectral density approach for the damping of fermion elementary excitations in an anisotropic spin- linear chain

Campana, L. S.; D'Auria, A. Caramico; D'Ambrosio, M.; Cesare, L. De; Esposito, U.

doi:10.1016/0378-4371(84)90116-x

Cited by 7 publications

(5 citation statements)

References 18 publications

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“…The method is based on a physically motivated ansatz for the single-electron spectral density. Its main advantages are the physically simple concept and the non-perturbative character being not restricted to Fermi-systems but also working for Bose-and even classical systems [24,25,26]. Recent applications of the SDA concern the attractive (U < 0) Hubbard model [27], the t − J model [28], the magnetism and electronic structure of systems of reduced dimensions as thin films and surfaces [29,30,31].…”

Section: Spectral Density Approachmentioning

confidence: 99%

Ferromagnetism within the Periodic Anderson Model: A New Approximation Scheme

Meyer¹,

Nolting²,

Reddy³

et al. 1998

phys. stat. sol. (b)

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We introduce a new approach to the periodic Anderson model (PAM) that allows a detailed investigation of the magnetic properties in the Kondo as well as the intermediate valence regime. Our method is based on an exact mapping of the PAM onto an effective medium strong-coupling Hubbard model. For the latter, the so-called spectral density approach (SDA) is rather well motivated since it is based on exact results in the strong coupling limit. Besides the T 0 phase diagram, magnetization curves and Curie temperatures are presented and discussed with help of temperature-dependent quasiparticle densities of state. In the intermediate valence regime, the hybridization gap plays a major role in determining the magnetic behaviour. Furthermore, our results indicate that ferromagnetism in this parameter regime is not induced by an effective spin±spin interaction between the localized levels mediated by conduction electrons as it is the case in the Kondo regime. The magnetic ordering is rather a single-band effect within an effective f-band.

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Section: Spectral Density Approachmentioning

confidence: 99%

Ferromagnetism within the Periodic Anderson Model: A New Approximation Scheme

Meyer¹,

Nolting²,

Reddy³

et al. 1998

phys. stat. sol. (b)

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Potthoff

Herrmann

Wegner

et al. 1998

phys. stat. sol. (b)

116

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The sum rule for the moments of the spectral density is discussed for the single-band Hubbard model. It is shown that respecting the sum rule up to the order m 3 is conceptually important for a qualitatively correct description of the quasi-particle band structure in the strong-correlation regime. Different analytical approximations for the self-energy are analyzed with respect to their compatibility with the moment sum rule. To estimate the practical usefulness of the sum rule, correlation functions and dynamical quantities are determined. The results obtained within the various approximation schemes of different complexity are compared with each other and also with essentially exact results available for infinite-dimensional lattices. It turns out that the m 3 moment is rather unimportant for the paramagnetic phase on the hyper-cubic lattice. Contrary, it decisively influences the magnetic phase boundary as well as the critical temperature for the ferromagnetic phase on an f.c.c.-type lattice.

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“…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.…”

Section: Spectral Density Approachmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

Magnetism in the single-band Hubbard model

Herrmann

Nolting

1997

Journal of Magnetism and Magnetic Materials

128

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A self-consistent spectral density approach (SDA) is applied to the Hubbard model to investigate the possibility of spontaneous ferro-and antiferromagnetism. Starting point is a two-pole ansatz for the single-electron spectral density, the free parameter of which can be interpreted as energies and spectral weights of respective quasiparticle excitations. They are determined by fitting exactly calculated spectral moments. The resulting self-energy consists of a local and a non-local part. The higher correlation functions entering the spin-dependent local part can be expressed as functionals of the single-electron spectral density. Under certain conditions for the decisive model parameters (Coulomb interaction U , Bloch-bandwidth W , band occupation n, temperature T ) the local part of the self-energy gives rise to a spin-dependent band shift, thus allowing for spontaneous band magnetism. As a function of temperature, second order phase transitions are found away from half filling, but close to half filling the system exhibits a tendency towards first order transitions. The non-local self-energy part is determined by use of proper two-particle spectral densities. Its main influence concerns a (possibly spin-dependent) narrowing of the quasiparticle bands with the tendency to stabilize magnetic solutions. The non-local self-energy part disappears in the limit of infinite dimensions. We present a full evaluation of the Hubbard model in terms of quasiparticle densities of states, quasiparticle dispersions, magnetic phase diagram, critical temperatures (TC , TN ) as well as spin and particle correlation functions. Special attention is focused on the non-locality of the electronic self-energy, for which some rigorous limiting cases are worked out.

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Spectral density approach for the damping of fermion elementary excitations in an anisotropic spin- linear chain

Cited by 7 publications

References 18 publications

Ferromagnetism within the Periodic Anderson Model: A New Approximation Scheme

Ferromagnetism within the Periodic Anderson Model: A New Approximation Scheme

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

Magnetism in the single-band Hubbard model

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