Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hierarchical mean-field approach to the $J_1$-$J_2$ Heisenberg model on
  a square lattice   We study the quantum phase diagram and excitation spectrum of the frustrated
$J_1$-$J_2$ spin-1/2 Heisenberg Hamiltonian. A hierarchical mean-field
approach, at the heart of which lies the idea of identifying {\it relevant}
degrees of freedom, is developed. Thus, by performing educated, manifestly
symmetry preserving mean-field approximations, we unveil fundamental properties
of the system. We then compare various coverings of the square lattice with
plaquettes, dimers and other degrees of freedom, and show that only the {\it
symmetric plaquette} covering, which reproduces the original Bravais lattice,
leads to the known phase diagram. The intermediate quantum paramagnetic phase
is shown to be a (singlet) {\it plaquette crystal}, connected with the
neighboring N\'eel phase by a continuous phase transition. We also introduce
fluctuations around the hierarchical mean-field solutions, and demonstrate that
in the paramagnetic phase the ground and first excited states are separated by
a finite gap, which closes in the N\'eel and columnar phases. Our results
suggest that the quantum phase transition between N\'eel and paramagnetic
phases can be properly described within the Ginzburg-Landau-Wilson paradigm.

8
The categories of this paper are: hep-ex
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci