Optimization of basis functions for the multi-configuration mixing using the Replica Exchange Monte-Carlo method and its application to 12C
Abstract
To calculate excited states in quantum many-body systems, multi-configuration mixing has often been employed. However, it has been still unclear how to choose important Slater determinants from a huge model space. We propose a novel efficient method as the Replica Exchange Monte-Carlo (RXMC) method to sample important Slater determinants and optimize and analyze the obtained results. As an application, we apply it to the ground and excited states of 12C based on the Bloch-Brink α cluster model and show the detailed structure of the obtained states. The RXMC method enables us to efficiently sample Slater determinants following the Boltzmann distribution on the multi-dimensional potential energy surface (PES) under a given model space. To analyze the obtained excited states, we embed sampled basis functions onto the PES calculated with the β-γ constraint method and discuss the main component in the state. The RXMC method can efficiently perform the samplings with a temperature parameter of TL=2.5 MeV in 12C. 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. 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 complicated nuclear fission dynamics in heavier nuclei.
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