Exploring Contractor Renormalization: Tests on the 2-D Heisenberg Antiferromagnet and Some New Perspectives

Abstract

Contractor Renormalization (CORE) is a numerical renormalization method for Hamiltonian systems that has found applications in particle and condensed matter physics. There have been few studies, however, on further understanding of what exactly it does and its convergence properties. The current work has two main objectives. First, we wish to investigate the convergence of the cluster expansion for a two-dimensional Heisenberg Antiferromagnet(HAF). This is important because the linked cluster expansion used to evaluate this formula non-perturbatively is not controlled by a small parameter. Here we present a study of three different blocking schemes which reveals some surprises and in particular, leads us to suggest a scheme for defining successive terms in the cluster expansion. Our second goal is to present some new perspectives on CORE in light of recent developments to make it accessible to more researchers, including those in Quantum Information Science. We make some comparison to entanglement-based approaches and discuss how it may be possible to improve or generalize the method.

Completely revised version accepted by Phy Rev B; 13 pages with added material on entropy in CORE

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• Numerical Contractor Renormalization Method for Quantum Spin Models
• Current Carrying Ground State in a Bi-layer Model
• Bond order wave instabilities in doped frustrated antiferromagnets: "Valence bond solids" at fractional filling
• Phase transitions in the Shastry-Sutherland lattice
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Cited by in corpus (10)

• A cluster-based mean-field and perturbative description of strongly correlated fermion systems. Application to the 1D and 2D Hubbard model
• Effective Spin Couplings in the Mott Insulator of the Honeycomb Lattice Hubbard Model
• Calculating excited states of molecular aggregates by the renormalized excitonic method
• Renormalization algorithm with graph enhancement
• Contractor-Renormalization approach to frustrated magnets in magnetic field
• Reducing Memory Cost of Exact Diagonalization using Singular Value Decomposition
• Strong-coupling expansion and effective hamiltonians
• Bootstrap Approximations in Contractor Renormalization
• Local renormalization method for random systems
• ENCORE: An Extended Contractor Renormalization algorithm