  The spin-orbit coupled double perovskite iridate Ba$_2$YIrO$_6$ with $d^4$
occupancy of Ir is considered as a candidate material for a non-magnetic $J=0$
ground state. The issue of existence of such a state in Ba$_2$YIrO$_6$ however
has opened up intense debates both in experimental and theoretical studies. In
this study, we revisit the issue using \textit{ab-initio} density functional
combined with dynamical mean-field theory to investigate the magnetic
properties of Ba$_2$YIrO$_6$ down to zero temperature. To reach the ground
state, a recently developed impurity solver based on tensor-product states
working directly at zero temperature is employed. We find that Ba$_2$YIrO$_6$
has a small instantaneous non-zero magnetic moment, both at $T=0$ K as well as
at room temperature. We did not observe any evidence of magnetic ordering, not
even at $T=0$ K. From the calculated local magnetic susceptibility we see that
the quantum fluctuations are very strong and effective in screening the
instantaneous moments. This dynamical screening, together with frustration
effects in the fcc lattice that can lead to almost degenerate magnetic ground
states, prevents any long-range ordering.
