Fokker-Planck equations have been applied in the past to field theory topics such as the stochastic quantization and the stabilization of bottomless action theories. In this paper we give another application of the FP-techniques in a way appropriate to the study of the ground state, the excited states and the critical behaviour of quantum lattice hamiltonians. Our approach is based on the choice of an exponential or Jastrow-like state which becomes the exact ground state of a discrete FP-hamiltonian. The "variational" parameters entering into the ansatz are fixed by forcing the FP-hamiltonian to coincide with the original hamiltonian except for terms not included in the ansatz. To illustrate the method we apply it to the Ising model in a transverse field (ITF). In one dimension we build up a FP-hamiltonian belonging to the same universality class as the standard ITF model. Likewise some considerations concerning the Potts model are outlined.
Jiménez, F., & Sierra, G. (1996). Fokker-planck approach to quantum lattice hamiltonians. Nuclear Physics B, 458(3), 640–668. https://doi.org/10.1016/0550-3213(95)00565-X