  Motivated by experimental studies that have found signatures of a quantum
spin liquid phase in organic crystals whose structure is well described by the
two-dimensional triangular lattice, we study the Hubbard model on this lattice
at half filling using the infinite-system density matrix renormalization group
(iDMRG) method. On infinite cylinders with finite circumference, we identify an
intermediate phase between observed metallic behavior at low interaction
strength and Mott insulating spin-ordered behavior at strong interactions.
Chiral ordering from spontaneous breaking of time-reversal symmetry, a
fractionally quantized spin Hall response, and characteristic level statistics
in the entanglement spectrum in the intermediate phase provide strong evidence
for the existence of a chiral spin liquid in the full two-dimensional limit of
the model.
