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arXiv · 2404.08581

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

Q. Y. Luo·X. Zhang·L. H. Chen·J. M. Yao
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Abstract

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.

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Q. Y. Luo, X. Zhang, L. H. Chen, J. M. Yao. 2024-04-12. Emulating generator coordinate method with extended eigenvector continuation: Lipkin-Meshkov-Glick model. https://doi.org/10.1103/physrevc.110.014309

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