Computing Effective Hamiltonians of Doped and Frustrated Antiferromagnets By Contractor Renormalization

TL;DR

This paper reviews the Contractor Renormalization (CORE) method for deriving low energy effective Hamiltonians, demonstrating its advantages over traditional methods and applying it to models relevant for high-Tc cuprates and frustrated antiferromagnets.

Contribution

It provides a systematic derivation of effective Hamiltonians using CORE, highlighting its benefits and applying it to complex magnetic systems and high-Tc superconductors.

Findings

Derivation of plaquette boson models for the 2D Hubbard model.

Prediction of spin-disordered, symmetry-breaking ground states in Kagome and Pyrochlore antiferromagnets.

Identification of a large density of low-energy singlet states.

Abstract

A review of the Contractor Renormalization (CORE) method, as a systematic derivation of the low energy effective hamiltonian, is given, with emphasis on its differences and advantages over traditional perturbative (weak/strong links) real space RG. For the low energy physics of the 2D Hubbard model, we derive the plaquette bosons (projected SO(5)) model which connects the microscopic model to phases and phenomenology of high-Tc cuprates. For the S=1/2 Pyrochlore and Kagome antiferromagnets, the effective hamiltonians predict spin-disordered, lattice symmetry breaking, ground states with a large density of low energy singlets as found by exact diagonalization of small clusters.