  Fluctuations in the initial transverse energy-density distribution lead to
anisotropic flows as observed in central high-energy heavy-ion collisions.
Studies of longitudinal fluctuations of the anisotropic flows can shed further
light on the initial conditions and dynamical evolution of the hot quark-gluon
matter in these collisions. Correlations between anisotropic flows with varying
pseudorapidity gaps in Pb+Pb collisions at the CERN Large Hadron Collider are
investigated using both an event-by-event (3+1)-D ideal hydrodynamical model
with fluctuating initial conditions and the a multiphase transport (AMPT) Monte
Carlo model for high-energy heavy-ion collisions. Anisotropic flows at
different pseudorapidities are found to become significantly decorrelated with
increasing pseudo-rapidity gaps due to longitudinal fluctuations in the initial
states of heavy-ion collisions. The longitudinal correlation of the elliptic
flow shows a strong centrality dependence while the correlation of the
triangular flow is independent of the centrality. Longitudinal fluctuations as
a source of the decorrelation are further shown to consist of a twist or
gradual rotation in flow angles between the forward and backward direction and
additional fluctuations on top of the twist. Within the AMPT model,
longitudinal correlations of anisotropic flows are also found to depend on the
value of partonic cross sections. The implicatiosn of constraining the initial
conditions and shear viscosity to entropy density ratio of the partonic matter
in high-energy heavy-ion collisions are also discussed.
