Spin-distribution functionals and correlation energy of the Heisenberg model

Details Spin-distribution functionals and correlation energy of the Heisenberg model Spin-distribution functionals and correlation energy of the Heisenberg model

2003-05-29

arxiv.org/abs/cond-mat/0305690v1

Phys. Rev. B 68, p. 024423 (2003)

Physics

Condensed Matter

Materials Science

9 pages, 5 figures, accepted for publication in Phys. Rev. B

Scientific paper

10.1103/PhysRevB.68.024423

We analyse the ground-state energy and correlation energy of the Heisenberg model as a function of spin, both in the ferromagnetic and in the antiferromagnetic case, and in one, two and three dimensions. First, we present a comparative analysis of known expressions for the ground-state energy $E_0(S)$ of {\it homogeneous} Heisenberg models. In the one-dimensional antiferromagnetic case we propose an improved expression for $E_0(S)$, which takes into account Bethe-Ansatz data for $S=1/2$. Next, we consider {\it inhomogeneous} Heisenberg models (e.g., exposed to spatially varying external fields). We prove a Hohenberg-Kohn-like theorem stating that in this case the ground-state energy is a functional of the spin distribution, and that this distribution encapsulates the entire physics of the system, regardless of the external fields. Building on this theorem, we then propose a local-density-type approximation that allows to utilize the results obtained for homogeneous systems also in inhomogeneous situations. We conjecture a scaling law for the dependence of the correlation functional on dimensionality, which is well satisfied by existing numerical data. Finally, we investigate the importance of the spin-correlation energy by comparing results obtained with the proposed correlation functional to ones from an uncorrelated mean-field calculation, taking as our example a linear spin-density wave state.

Affiliated with

Also associated with

No associations

Rating

Spin-distribution functionals and correlation energy of the Heisenberg model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Spin-distribution functionals and correlation energy of the Heisenberg model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spin-distribution functionals and correlation energy of the Heisenberg model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-607278