General correction theorems on decomposition formulae of exponential operators and extrapolation methods for quantum Monte Carlo simulations

It is proved that the trace of the generalized Trotter formula $\text{Z(n) ≡ Tr[II exp(}\text{A}{}_{\mathrm{j}}\text{n]}{}^{\mathrm{n}}$ is an even function of n, when all A_j are symmetric, namely A^t_j = A_j, togethern with some generalizations. This yields a new extrapolatio n method of the form $\text{Z(n) ? Z(∞) + a/(n}{}^2\text{+ b)}$ for large n in quanntum Monte Carlo simulations.