Berry phase of many-body system: time-dependent representation method

In this paper, we investigate the Berry phase of many-body system in the time-dependent representation. The formula of Berry phase of many-body system calculating in the time-dependent representation is derived. In this scenario, the Berry phase can be decomposed into two terms, which have different physical meanings respectively. Using these formula, we calculated the Berry phase for the many-spin system coupled by the XXZ exchange interaction. The results show that the Berry phase consists of two contributions which can be interpreted as the flux of a nonquantized monopole and the flux of a Dirac ring respectively