{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T10:28:15Z","timestamp":1648895295433},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"14","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Mod. Phys. B"],"published-print":{"date-parts":[[2013,6,10]]},"abstract":"<jats:p> The four site and eight site 1D anti-ferromagnetic Heisenberg chains in the Jordan\u2013Wigner representation are investigated within the standard Hartree\u2013Fock and random phase approximation (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. <\/jats:p>","DOI":"10.1142\/s0217979213500586","type":"journal-article","created":{"date-parts":[[2013,5,9]],"date-time":"2013-05-09T08:39:57Z","timestamp":1368088797000},"page":"1350058","source":"Crossref","is-referenced-by-count":0,"title":["THE 1D HEISENBERG ANTIFERROMAGNET MODEL BY THE VARIATION AFTER PROJECTION METHOD"],"prefix":"10.1142","volume":"27","author":[{"given":"AZIZ","family":"RABHI","sequence":"first","affiliation":[{"name":"CFC, Departamento de F\u00edsica, Universidade de Coimbra, 3004-516 Coimbra, Portugal"},{"name":"LPMC-FST, Universit\u00e9 de Tunis El-Manar, Campus Universitaire, Le Belv\u00e9d\u00e8re-1060, Tunisia"}]},{"given":"MARTA","family":"BRAJCZEWSKA","sequence":"additional","affiliation":[{"name":"CFC, Departamento de F\u00edsica, Universidade de Coimbra, 3004-516 Coimbra, Portugal"}]},{"given":"PETER","family":"SCHUCK","sequence":"additional","affiliation":[{"name":"Institut de Physique Nucl\u00e9aire, IN2P3-CNRS, Universit\u00e9 Paris-Sud, F-91406 Orsay Cedex, France"},{"name":"LPM2C, Maison des Magist\u00e8res-CNRS, 25, av. des Martyrs, BP 166, 38042, Grenoble Cedex, France"}]},{"given":"JO\u00c3O","family":"DA PROVID\u00caNCIA","sequence":"additional","affiliation":[{"name":"CFC, Departamento de F\u00edsica, Universidade de Coimbra, 3004-516 Coimbra, Portugal"}]},{"given":"RAOUF","family":"BENNACEUR","sequence":"additional","affiliation":[{"name":"LPMC-FST, Universit\u00e9 de Tunis El-Manar, Campus Universitaire, Le Belv\u00e9d\u00e8re-1060, Tunisia"}]}],"member":"219","published-online":{"date-parts":[[2013,5,19]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01328601"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01341708"},{"key":"rf3","doi-asserted-by":"crossref","unstructured":"H.J.\u00a0Mikeska and A. 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