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Physica A Statistical Mechanics and its Applications

Quantum Monte Carlo methods and general decomposition theory of exponential operators and symplectic integrators

Masuo Suzuki

Published Apr 1, 1994• 17 citations
Publisher
DOI
10.1016/0378-4371(94)90491-x

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A general scheme of fractal decomposition of exponential operators is presented in any order m. Namely, exp[x(A+B)]=Sm(x)+O(xm+1) for any positive integer m, where Sm(x)=et1A et2B et3A et4B⋅⋅⋅etMA with finite M depending on m. A general recursive scheme of construction of {tj} is given explicitly. It is proven that some of {tj} should be negative for m≥3 and for any finite M (nonexistence theorem of positive decomposition). General systematic decomposition criterions based on a new type of time-ordering are also formulated. The decomposition exp[x(A+B)]=[Sm(x/n)]n +O(xm+1/nm) yields a new efficient approach to quantum Monte Carlo simulations.