  A recent focus of quantum spin liquid (QSL) studies is how
disorder/randomness in a QSL candidate affects its true magnetic ground state.
The ultimate question is whether the QSL survives disorder or the disorder
leads to a "spin-liquid-like" state, such as the proposed random-singlet (RS)
state. Since disorder is a standard feature of most QSL candidates, this
question represents a major challenge for QSL candidates. YbMgGaO$_4$, a
triangular lattice antiferromagnet with effective spin-1/2 Yb$^{3+}$ ions, is
an ideal system to address this question, since it shows no long-range magnetic
ordering with Mg/Ga site disorder. Despite the intensive study, it remains
unresolved as to whether YbMgGaO$_4$ is a QSL or in the RS state. Here, through
ultralow-temperature thermal conductivity and magnetic torque measurements,
plus specific heat and DC magnetization data, we observed a residual
$\kappa_0/T$ term and series of quantum spin state transitions in the zero
temperature limit for YbMgGaO$_4$. These observations strongly suggest that a
QSL state with itinerant excitations and quantum spin fluctuations survives
disorder in YbMgGaO$_4$.
