  The critical breakdown of a one-dimensional quantum magnet with long-range
interactions is studied by investigating the high-field polarized phase of the
anisotropic XY model in a transverse field for the ferro- and antiferromagnetic
case. While for the limiting case of the isotropic long-range XY model we can
extract the elementary one quasi-particle dispersion analytically and calculate
two quasi-particle excitation energies quantitatively in a numerical fashion,
for the long-range Ising limit as well as in the intermediate regime we use
perturbative continuous unitary transformations on white graphs in combination
with classical Monte Carlo simulations for the graph embedding to extract
high-order series expansions in the thermodynamic limit. This enables us to
determine the quantum-critical breakdown of the high-field polarized phase by
analyzing the gap-closing including associated critical exponents and
multiplicative logarithmic corrections. In addition, for the ferromagnetic
isotropic XY model we determined the critical exponents $z$ and $\nu$
analytically by a bosonic quantum-field theory.
