Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Velocity of excitations in ordered, disordered and critical
  antiferromagnets   We test three different approaches, based on quantum Monte Carlo simulations,
for computing the velocity $c$ of triplet excitations in antiferromagnets. We
consider the standard $S=1/2$ one- and two-dimensional Heisenberg models, as
well as a bilayer Heisenberg model at its critical point. Computing correlation
functions in imaginary time and using their long-time behavior, we extract the
lowest excitation energy versus momentum using improved fitting procedures and
a generalized moment method. The velocity is then obtained from the dispersion
relation. We also exploit winding numbers to define a cubic space-time
geometry, where the velocity is obtained as the ratio of the spatial and
temporal lengths of the system when all winding number fluctuations are equal.
The two methods give consistent results for both ordered and critical systems,
but the winding-number estimator is more precise. For the Heisenberg chain, we
accurately reproduce the exactly known velocity. For the two-dimensional
Heisenberg model, our results are consistent with other recent calculations,
but with an improved statistical precision; $c=1.65847(4)$. We also use the
hydrodynamic relation $c^2=\rho_s/\chi_\perp(q\to 0)$ between $c$, the spin
stiffness $\rho_s$, and the transversal susceptibility $\chi_\perp$, using the
smallest non-zero momentum $q=2\pi/L$. This method also is well controlled in
two dimensions, but the cubic criterion for winding numbers delivers better
numerical precision. In one dimension the hydrodynamic relation is affected by
logarithmic corrections which make accurate extrapolations difficult. As an
application of the winding-number method, for the quantum-critical bilayer
model our high-precision determination of the velocity enables us to
quantitatively test, at an unprecedented level, field-theoretic predictions for
low-temperature scaling forms where $c$ enters.

1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci