  We present a benchmark study of generator coordinate method (GCM) combined
with eigenvector continuation (EC) in two different schemes for the low-lying
states of Lipkin-Meshkov-Glick (LMG) model, where the interaction strength is
treated as a controlling parameter, simulating quantum many-body systems with
the phase transition from non-collective to collective states. We demonstrate
that the EC$_{\rm kmax}$ scheme accurately reproduces the low-lying states of
the LMG model. In this scheme, the EC basis consists of the wave functions of
low-lying states up to the $k_{\rm max}$-th state of sampling Hamiltonians.
Compared to EC$_1$, which only includes the wave functions of the $k$-th state
of sampling Hamiltonians for the $k$-th state of a target Hamiltonian, the
EC$_{\rm kmax}$ scheme exhibits significantly improved efficiency and accuracy.
This study suggests the potential utilization of the extended EC scheme as an
efficient emulator for GCM calculations.
