  By precisely writing down the matrix element of the local Boltzmann operator,
we have proposed a new path integral formulation for quantum field theory and
developed a corresponding Monte Carlo algorithm. With current formula, the
Hubbard-Stratonovich transformation is not necessary, and is not based on the
determinant approach, which can improve the computational efficiency. The
results show that, the simulation time has the square-law scaling with system
sizes, which is comparable with the usual first-principle calculation. The
current formula also improves the accuracy of the Suzuki-Trotter decomposition.
As an example, we have studied the one-dimensional half-filled Hubbard model at
finite temperature. The obtained results are in excellent agreement with the
known solutions. The new formula and Monte Carlo algorithm can be used in
various studies.
