Contractor renormalization group and the Haldane conjecture - art. no. 174421

The contractor renormalization group formalism (CORE) is a real-space renor malization group method which is the Hamiltonian analogue of the Wilson exa ct renormalization group equations. In an earlier paper [Phys. Rev. D 61, 0 34505 (2000)] I showed that the CORE method could be used to map a theory o f free quarks and quarks interacting with gluons into a generalized frustra ted Heisenberg antiferromagnet (HAF) and proposed using CORE methods to stu dy these theories. Since generalizations of HAF's exhibit all sorts of subt le behavior which, from a continuum point of view, are related to topologic al properties of the theory, it is important to know that CORE can be used to extract this physics. In this paper I show that despite the folklore whi ch asserts that all real-space renormalization group schemes are necessaril y inaccurate, simple CORE computations can give highly accurate results eve n if one only keeps a small number of states per block and a few terms in t he cluster expansion. In addition I argue that even very simple CORE comput ations give a much better qualitative understanding of the physics than nai ve renormalization group methods. In particular I show that the simplest CO RE computation yields a first-principles understanding of how the famous Ha ldane conjecture works for the case of the spin-1/2 and spin-1 HAF.