FokkerPlanck approach to quantum lattice hamiltonians
Abstract
FokkerPlanck 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 FPtechniques 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 Jastrowlike state which becomes the exact ground state of a discrete FPhamiltonian. The "variational" parameters entering into the ansatz are fixed by forcing the FPhamiltonian 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 FPhamiltonian belonging to the same universality class as the standard ITF model. Likewise some considerations concerning the Potts model are outlined.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1996
 DOI:
 10.1016/05503213(95)00565X
 arXiv:
 arXiv:condmat/9504012
 Bibcode:
 1996NuPhB.458..640J
 Keywords:

 Condensed Matter;
 High Energy Physics  Theory
 EPrint:
 42 pages, LaTeX, 3 figures available upon request