Emulating the generator coordinate method with extended eigenvector continuation for the Lipkin-Meshkov-Glick model

We present a benchmark study of the generator coordinate method (GCM) combined with eigenvector continuation (EC) in two different schemes for the low-lying states of the 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 noncollective to collective states. We demonstrate that the ECₖₘₐₓ 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 kₘₐₓ-th state of sampling Hamiltonians. Compared to EC₁, which only includes the wave functions of the kth state of sampling Hamiltonians for the kth state of a target Hamiltonian, the ECₖₘₐₓ 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.