  Ground- and excited-state quantum fidelities in combination with generalized
quantum fidelity susceptibilites, obtained from exact diagonalizations, are
used to explore the phase diagram of the anisotropic next-nearest-neighbour
triangular Heisenberg model. Specifically, the $J'-J_2$ plane of this model,
which connects the $J_1-J_2$ chain and the anisotropic triangular lattice
Heisenberg model, is explored using these quantities. Through the use of a
quantum fidelity associated with the first excited-state, in addition to the
conventional ground-state fidelity, the BKT-type transition and Majumdar-Ghosh
point of the $J_1-J_2$ chain ($J'=0$) are found to extend into the $J'-J_2$
plane and connect with points on the $J_2=0$ axis thereby forming bounded
regions in the phase diagram. These bounded regions are then explored through
the generalized quantum fidelity susceptibilities $\chi_{\rho}$,
$\chi_{120^{\circ}}$, $\chi_D$ and $\chi_{CAF}$ which are associated with the
spin stiffness, $120^{\circ}$ spiral order parameter, dimer order parameter and
collinear antiferromagnetic order parameter respectively. These quantities are
believed to be extremely sensitive to the underlying phase and are thus well
suited for finite-size studies. Analysis of the fidelity susceptibilities
suggests that the $J',J_2 \ll J$ phase of the anisotropic triangular model is
either a collinear antiferromagnet or possibly a gapless disordered phase that
is directly connected to the Luttinger phase of the $J_1-J_2$ chain.
Furthermore, the outer region is dominated by incommensurate spiral physics as
well as dimer order.
