Energy-variance minimization for ground and excited states in the Lipkin model and its application to molecular magnets

Abstract

This work introduces a variational method for accurately determining both ground and excited states in systems describedby the Lipkin model. Traditional variational techniques often struggle to capture excited states because they tend to convergeto the lowest energy solution, a phenomenon known as variational collapse. To address this, we employ an energy-varianceminimization approach, which treats all states on equal footing and prevents the method from favoring the ground state.Several functional forms for wave functions are explored, including a self-consistent mean-field ansatz, a coupled-cluster-inspired formulation, and an extended coupled-cluster ansatz. The latter approach improves accuracy by incorporatingcorrelations into the reference state with minimal computational cost, leading to wave functions that closely approximateexact solutions. The proposed methodology is applied to a molecular magnet, specifically a cation Fe8 cluster, incorporatingmagnetic anisotropy. The results as functions of the applied magnetic field demonstrate the effectiveness of this approach inproviding an accurate and efficient description of energy spectra of these systems.