The 1D Heisenberg antiferromagnet model by the variation after projection method

The 4 sites and 8 sites 1D anti-ferromagnetic Heisenberg chains in the Jordan-Wigner representation are investigated within the standard Hartree-Fock and RPA approaches, both in the symmetry unbroken and in the symmetry broken phases. A translation invariant groundstate, obtained by the projection method as a linear combination of a symmetry-broken HF state and its image under reflection, is also considered, for each chain type. It is found that the projection method considerably improves the HF treatment for instance as far as the groundstate energy is concerned, but also with respect to the RPA energies. The results are furthermore confronted with the ones obtained within so-called SCRPA scheme.Comment: 15 pages, 8 figures, 1 table, accepted for publication in Int. J. Mod. Phys.

Expansao em bosoes termicos no modelo de Heisenberg

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Expansão em bosões térmicos no modelo de Heisenberg

Neste trabalho, o método de expansão em bosões térmicos (TBE) é estudado e aplicado no domínio do magnetismo. Recorreu-se ao modelo de Heisenberg para um conjunto de spins localizados numa rede cristalina. Os graus de liberdade intrínsecos do sistema são descritos na aproximação do campo médio, enquanto os graus de liberdade colectivos são descritos por meio de bosões. A TBE possibilita a definição de ondas de spin a temperatura finita, alargando assim a aplicação da teoria dos magnões até à vizinhança da temperatura crítica. Este trabalho discute o problema cinemático da teoria das ondas de spin. Mostra-se aqui que um ingrediente essencial da resolução do problema cinemático reside na redução do espaço de fase acessível aos magnões, em particular para S >= 1. É efectuada uma comparação com as outras teorias de renormalização dos magnões, nomeadamente com a renormalização cinemática da aproximação de fases aleatórias (RPA) e a renormalização dinâmica da aproximação dos magnões renormalizados (MRA). Comparam-se também os resultados obtidos com alguns dados experimen-tais para os compostos EuO, EuS e MnF2

Self-expansion and compression of charged clusters of stabilized jellium

In a positively charged metallic cluster, surface tension tends to enhance the ionic density with respect to its bulk value, while surface-charge repulsion tends to reduce it. Using the stabilized jellium model, we examine the self-expansion and compression of positively charged clusters of simply metals. Quantal results from the Kohn-Sham equations using the local density approximation are compared with continuous results from the liquid drop model. The positive background is constrained to a spherical shape. Numerical results for the equilibrium radius and the elastic stiffness are presented for singly and doubly positively charged aluminum, sodium, and cesium clusters of 1-20 atoms. Self-expansion occurs for small charged clusters of sodium and cesium, but not of aluminum. The effect of the expansion or compression on the ionization energies is analyzed. For Al6, we also consider net charges greater than 2+. The results of the stabilized jellium model for self-compression are compared with those of other models, including the SAPS (spherical averaged pseudopotential model

Ionization energy and electron affinity of a metal cluster in the stabilized jellium model: Size effect and charging limit

We report the first reliable theoretical calculation of the quantum size correction c which yields the asymptotic ionization energy I(R) = W + ((1/2) + c)/R + O(R–2) of a simple-metal cluster of radius R. Restricted-variational electronic density profiles are used to evaluate two sets of expressions for the bulk work function W and quantum size correction c: the Koopmans expressions, and the more accurate and profile-insensitive Delta SCF expressions. We find c [approximate] –0.08 for stabilized (as for ordinary) jellium, and thus for real simple metals. We present parameters from which the density profiles may be reconstructed for a wide range of cluster sizes, including the planar surface. We also discuss how many excess electrons can be bound by a neutral cluster of given size. Within a continuum picture, the criterion for total-energy stability of a negatively charged cluster is less stringent than that for existence of a self-consistent solutio

Collective and intrinsic degrees of freedom in the Heisenberg ferromagnet.

A separation between collective and intrinsic degrees of freedom in the Heisenberg model of a ferromagnet at a finite temperature is achieved by reformulating the thermal boson expansion previously obtained by the present authors. In the new approach, all the collective modes (spin waves) have wavenumbers lower than a certain value. The intrinsic energy turns out to be the usual mean-field energy minus a correlation energy due to the excitations of spin waves. The influence of the cutoff in momentum space on the critical temperature is studied and the temperature dependence of the spin-wave renormalisation factor and the magnetisation are calculated