Lagrange approach in stochastic quantization of the 2D Hubbard model

A new method of the generation of Green's function in external local and bilocal fields is proposed for the stochastic quantization of the 2D Hubbard model. The differential equations for Green's functions transform to the system of integral equations and it is solved numerically for a local Hubbard-Stratanovich field. The Trotter-Suzuki expansion and the matrix elements of the evolution operator are not used in this approach. For a 4x4 lattice with half-filled band the total energy E, the density n, the density-density [n(i up arrow)n(i down arrow)] and spin-spin [(SiSjz)-S-z] correlation functions were calculated by stochastic quantization as the functions of one-site repusion U and inverse temperature beta. The obtained results are in agreement with the previous Monte Carlo calculations.