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

Abstract

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.

15 pages, 8 figures, 1 table, accepted for publication in Int. J. Mod. Phys. B

References in corpus (6)

• One-Dimensional Magnetism
• Boson-Fermion pairing in Bose-Fermi mixtures on 1D optical lattices
• Self-Consistent Random Phase Approximation - Application to the Hubbard Model for finite number of sites
• Pair Fluctuations in Ultra-small Fermi Systems within Self-Consistent RPA at Finite Temperature
• Self-Consistent Quasi-Particle RPA for the Description of Superfluid Fermi Systems
• Random phase approximation for the 1D anti-ferromagnetic Heisenberg model