Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entanglement and fluctuations in the XXZ model with power-law
  interactions   We investigate the ground-state properties of the XXZ model with
$1/r^{\alpha}$ interactions, describing spins interacting with long-range (LR)
transverse (XX) ferromagnetic interactions and longitudinal (Z)
antiferromagnetic interactions, or hardcore bosons with LR repulsion and
hopping. The LR nature of the couplings allows us to quantitatively study the
spectral, correlation and entanglement properties of the system by making use
of linear spin-wave theory, supplemented with density-matrix renormalization
group in one-dimensional systems. Our most important prediction is the
existence of three distinct coupling regimes, depending on the decay exponent
$\alpha$ and number of dimensions $d$: 1) a short-range regime for $\alpha > d
+ \sigma_c$ (where $\sigma_c = 1$ in the gapped N\'eel antiferromagnetic phase
exhibited by the XXZ model, and $\sigma_c = 2$ in the gapless XY ferromagnetic
phase), sharing the same properties as those of finite-range interactions
($\alpha=\infty$); 2) a long-range regime $\alpha < d$, sharing the same
properties as those of the infinite-range interactions ($\alpha=0$) in the
thermodynamic limit; and 3) a most intriguing medium-range regime for $d <
\alpha < d+\sigma_c$, continuously interpolating between the finite-range and
the infinite-range behavior. The latter regime is characterized by elementary
excitations with a long-wavelength dispersion relation $\omega \approx \Delta_g
+ ck^z$ in the gapped phase, and $\omega \sim k^z$ in the gapless phase,
exhibiting a continuously varying dynamical exponent $z = (\alpha - d) /
\sigma_c$. In the gapless phase of the model the $z$ exponent is found to
control the scaling of fluctuations, the decay of correlations, and a universal
sub-dominant term in the entanglement entropy, leading to a very rich palette
of behaviors for ground-state quantum correlations beyond what is known for
finite-range interactions.

23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph