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

TL;DR

This paper investigates small 1D antiferromagnetic Heisenberg chains using Hartree-Fock, RPA, and projection methods, demonstrating that the projection approach significantly enhances energy estimates compared to traditional methods.

Contribution

It introduces a projection method to improve Hartree-Fock and RPA results for 1D Heisenberg chains, comparing with SCRPA schemes.

Findings

Projection method improves groundstate energy estimates.

Projection method enhances RPA energy accuracy.

Results show better agreement with exact solutions.

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.