Error bound in trace norm for Trotter–Kato product formula of Gibbs semigroups

We study the error bound in the trace norm for the Trotter–Kato exponential product formula of Schrödinger semigroups with a certain class of singular potentials. The error bound heavily depends on the growth and smoothness properties of potentials. As an application, we can also obtain the error estimate in calculating an approximate value of partition function, which is one of the most important quantities in quantum statistical mechanics, by use of the exponential product formula.