  Based on $4.481\times10^8$ $\psi(3686)$ events collected with the BESIII
detector at BEPCII, the branching fraction of the isospin violating decay
$\psi(3686)\rightarrow\bar{\Sigma}^{0}\Lambda+c.c.$ is measured to be $(1.60
\pm 0.31 \pm 0.13~\pm~0.58) \times 10^{-6}$, where the first uncertainty is
statistical, the second is systematic, and the third is the uncertainty arising
from interference with the continuum. This result is significantly smaller than
the measurement based on CLEO-c data sets. The decays $\chi_{cJ}
\rightarrow\Lambda\bar{\Lambda}$ are measured via
$\psi(3686)\rightarrow\gamma\chi_{cJ}$, and the branching fractions are
determined to be
$\mathcal{B}\left(\chi_{c0}\rightarrow\Lambda\bar{\Lambda}\right)=(3.64 \pm
0.10 \pm 0.10 \pm 0.07)\times 10^{-4}$,
$\mathcal{B}\left(\chi_{c1}\rightarrow\Lambda\bar{\Lambda}\right)=(1.31\pm0.06
\pm 0.06 \pm0.03)\times 10^{-4}$,
$\mathcal{B}\left(\chi_{c2}\rightarrow\Lambda\bar{\Lambda}\right)=(1.91\pm0.08
\pm 0.17 \pm0.04)\times 10^{-4}$, where the third uncertainties are systematic
due to the $\psi(3686) \rightarrow \gamma \chi_{c J}$ branching fractions.
