Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pseudo-Goldstone gaps and order-by-quantum-disorder in frustrated
  magnets   In systems with competing interactions, continuous degeneracies can appear
which are accidental, in that they are not related to any symmetry of the
Hamiltonian. Accordingly, the pseudo-Goldstone modes associated with these
degeneracies are also unprotected. Indeed, through a process known as
"order-by-quantum-disorder", quantum zero-point fluctuations can lift the
degeneracy and induce a gap for these modes. We show that this gap can be
exactly computed at leading order in $1/S$ in spin-wave theory from the mean
curvature of the classical and quantum zero-point energies - without the need
to consider any spin-wave interactions. We confirm this equivalence through
direct calculations of the spin-wave spectrum to $O(1/S^2)$ in a wide variety
of theoretically and experimentally relevant quantum spin models. We prove this
equivalence through the use of an exact sum rule that provides the required
mixing of different orders of $1/S$. Finally, we discuss some implications for
several leading order-by-quantum-disorder candidate materials, clarifying the
expected pseudo-Goldstone gap sizes in Er$_2$Ti$_2$O$_7$ and
Ca$_3$Fe$_2$Ge$_3$O$_{12}$.

0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio