The geometric phase of the bipartite system is a sum over the one-particle geometric phase for the subsystems Schmidt decomposition Y()=VP, IE, ()@le, (0)2 For the composite system evolving adiabatically The one particle geometric phase ∑+2/2 of subsystem 1 (1)|e1(m)d Berry phase of the whole system iEOITE()dt13 1 2 | ( ) | ( ) | ( ) j j j j Schmidt decomposition   =    t p E t e t  For the composite system evolving adiabatically j j j j 1, 2, j j    = +   p p Berry phase of the whole system 0 ( ) | ( ) T j j i E t E t dt t      0 ( ) | ( ) T j j i e t e t dt t      The ‘one particle geometric phase’ of subsystem 1 The geometric phase of the bipartite system is a sum over the one-particle geometric phase for the subsystems