Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $ab$-$initio$ Approaches for Low-Energy Spin Hamiltonians   Implicit in the study of magnetic materials is the concept of spin
Hamiltonians, which emerge as the low-energy theories of correlation-driven
insulators. In order to predict and establish such Hamiltonians for real
materials, a variety of first principles $ab$-$initio$ methods have been
developed, based on density functional theory and wavefunction methodologies.
In this review, we provide a basic introduction to such methods and the
essential concepts of low-energy Hamiltonians, with a focus on their practical
capabilities and limitations. We further discuss our recent efforts toward
understanding a variety of complex magnetic systems that present unique
challenges from the perspective of $ab$-$initio$ approaches.

5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol