  As one of the most intriguing states of matter, the chiral spin liquid (CSL)
has attracted much scientific interest. On one hand, its existence and
mechanism in crystalline strongly correlated systems remain hotly debated. On
the other hand, strong correlation driven emergent phenomena can be realized in
twisted transition-metal dichalcogenide bilayers with a tremendously tunable
large length scale providing a new platform for the emergence of CSLs. We focus
on a strongly correlated model relevant to heterobilayer
$\textrm{WSe}_{2}/\textrm{MoSe}_{2}$ and investigate the Mott insulating phase
at half filling under an out-of-plane magnetic field. Considering both its
orbital and spin Zeeman effects we identify three conventionally ordered phases
including a $120^{\circ}$ Ne\'{e}l phase, a stripe phase and an up-up-down
phase. For intermediate fields an emergent quantum spin liquid phase is
identified with partial spin polarization. We further characterize the
topological nature of the quantum spin liquid as the $\nu$ = 1/2 Laughlin
chiral spin liquid through the topological entanglement spectrum and quantized
spin pumping under spin flux insertion. In addition, we map out the quantum
phase diagram for different twisted angles in an experimentally accessible
parameter regime.

Strongly Correlated Electrons;Materials Science