  We study quantum phase transitions in Heisenberg antiferromagnetic chains
with a staggered power-law decaying long-range interactions. Employing the
density-matrix renormalization group (DMRG) algorithm and the fidelity
susceptibility as the criticality measure, we establish more accurate values of
quantum critical points than the results obtained from the spin-wave
approximation, quantum Monte Carlo and DMRG in literatures. The deviation is
especially evident for strong long-range interactions. We extend isotropic
long-range interactions to the anisotropic cases and find that kaleidoscope of
quantum phases emerge from the interplay of anisotropy of the long-range
exchange interaction and symmetry breaking. We demonstrate nonfrustrating
long-range interactions induce the true long-range order in Heisenberg
antiferromagnetic chains with a continuous symmetry breaking, lifting the
restrictions imposed by the Mermin-Wagner theorem.
