Evolution of the single-hole spectral function across a quantum phase transition in the anisotropic-triangular-lattice antiferromagnet

We study the evolution of the single-hole spectral function when the ground state of the anisotropic-triangular-lattice antiferromagnet changes from the incommensurate magnetically-ordered phase to the spin-liquid state. In order to describe both of the ground states on equal footing, we use the large-$N$ approach where the transition between these two phases can be obtained by controlling the quantum fluctuations via an `effective' spin magnitude. Adding a hole into these ground states is described by a $t$-$J$ type model in the slave-fermion representation. Implications of our results to possible future ARPES experiments on insulating frustrated magnets, especially Cs$_2$CuCl$_4$, are discussed.