Contractor renormalization group and the Haldane conjecture

Journal Article · Tue May 01 04:00:00 EDT 2001 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.63.174421· OSTI ID:40205501

Weinstein, Marvin

The contractor renormalization group formalism (CORE) is a real-space renormalization group method which is the Hamiltonian analogue of the Wilson exact renormalization group equations. In an earlier paper [Phys. Rev. D 61, 034505 (2000)] I showed that the CORE method could be used to map a theory of free quarks and quarks interacting with gluons into a generalized frustrated Heisenberg antiferromagnet (HAF) and proposed using CORE methods to study these theories. Since generalizations of HAF's exhibit all sorts of subtle behavior which, from a continuum point of view, are related to topological 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 which asserts that all real-space renormalization group schemes are necessarily inaccurate, simple CORE computations can give highly accurate results even if one only keeps a small number of states per block and a few terms in the cluster expansion. In addition I argue that even very simple CORE computations give a much better qualitative understanding of the physics than naive renormalization group methods. In particular I show that the simplest CORE computation yields a first-principles understanding of how the famous Haldane conjecture works for the case of the spin-1/2 and spin-1 HAF.

• Sponsoring Organization: (US)
• OSTI ID: 40205501
• Journal Information: Physical Review B, Journal Name: Physical Review B Journal Issue: 17 Vol. 63; ISSN 0163-1829
• Publisher: The American Physical Society
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CLUSTER EXPANSION
CONTRACTORS
GLUONS
HAMILTONIANS
PHYSICS
QUARKS
RENORMALIZATION