Small moments without long-range magnetic ordering in the zero-temperature ground state of the double perovskite iridate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Ba</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>YIrO</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:mrow></mml:math>

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