Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Topological Excitations: from the Sawtooth Lattice to the
  Heisenberg Chain   The recently elucidated structure of the delafossite YCuO$_{2.5}$ reveals a
Cu-O network with nearly independent $\Delta$ chains having different
interactions between the $s=1/2$ spins. Motivated by this result, we study the
$\Delta$ chain for various ratios $J_{\rm bb}/J_{\rm bv}$ of the base-base and
base-vertex interactions. By exact diagonalization and extrapolation, we show
that the elementary excitation spectrum, which (within numerical error) is the
same for total spins $S_{\rm tot}=0$ and 1, has a gap only in the interval
$0.4874(1) \leq J_{\rm bb}/J_{\rm bv} \leq 1.53(1)$. The gap is dispersionless
for $J_{\rm bb}/J_{\rm bv}=1$, but has increasing $k$-dependence as $J_{\rm
bb}/J_{\rm bv}$ moves away from unity, related to the instability of dimers in
the ground state.

27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
1
The categories of this paper are: cs