Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations

A new systematic scheme of decomposition of exponential operators is presented, namely exp [ x( A+ B)]= S_m( x)+O( x^m+1 ) for any positive integer m, where S_m( x)=e ^{t1 A}e ^{t2 B}e ^{t3 A}e ^{t4 B}…e ^tMA. A general scheme of construction of { t _j} is given explicitly. The decomposition exp[ x( A+ B)]=[ S_m( x/ n)] ⁿ+O( x^m+1 / n^m) yields a new efficient approach to quantum Monte Carlo simulations.