Optimization of basis functions for multiconfiguration mixing using the replica exchange Monte Carlo method and its application to C12

Abstract

Background: To calculate excited states in quantum many-body systems, multiconfiguration mixing has often been employed. However, it remains unclear how to choose important Slater determinants from a huge model space.Purpose: We propose an efficient method as the replica exchange Monte Carlo (RXMC) method to sample important Slater determinants and optimize and analyze the results obtained. As an application, we investigate the ground and excited states of $^{12}\mathrm{C}$ based on the Bloch-Brink $\ensuremath{\alpha}$ cluster model and show the detailed structure of the obtained states.Methods: The RXMC method enables us to efficiently sample Slater determinants following the Boltzmann distribution on the multidimensional potential-energy surface (PES) under a given model space. To analyze the excited states obtained, we embed sampled basis functions onto the PES calculated with the $\ensuremath{\beta}\text{\ensuremath{-}}\ensuremath{\gamma}$ constraint method and discuss the main component in each state.Results: The RXMC method efficiently performs the samplings with a temperature parameter of ${T}_{L}=2.5$ MeV in $^{12}\mathrm{C}$. We obtain the gas-like state with a wide density distribution in the tail part in the second ${0}^{+}$ state. We also obtain the linear-chain-like states with the bending and stretching vibrational modes in the third and fourth ${0}^{+}$ states, respectively. In the fifth ${0}^{+}$ state, the main component of the basis functions contains expanded equilateral-triangle configurations.Conclusions: The second ${0}^{+}$ gas-like state emerges at the local minimum in the PES, which is the beginning of the valley structure connected to the linear-chain breakup channel. The third and fourth linear-chain-like states emerge in this valley structure. We conclude that the RXMC method is a powerful method to calculate the excited states of nuclei, which would be applied to much more complicated nuclear fission dynamics in heavier nuclei.