Applications of the generalized Trotter formula

We study the properties of Suzuki's systematic approximations to the exponential operator $\mathrm{exp}(\ensuremath{-}\ensuremath{\beta}H)$ by calculating the thermodynamic functions of three simple quantum models. We demonstrate that the path-integral representation of the partition function obtained from these approximations can be simplified and made more accurate by constructing Hermitian versions of Suzuki's expressions.