Numerical Contractor Renormalization applied to strongly correlated systems

TL;DR

This paper demonstrates the use of the Contractor Renormalization (CORE) method to derive effective Hamiltonians for strongly correlated quantum systems, enabling numerical analysis of complex models like frustrated magnets.

Contribution

It introduces a numerical approach combining CORE with finite-size scaling to study strongly correlated systems, providing a semi-quantitative tool for complex quantum models.

Findings

Effective Hamiltonians can be constructed for complex systems.

Finite-size extrapolations yield thermodynamic limit results.

Applicable to frustrated magnets and doped systems.

Abstract

We demonstrate the utility of effective Hamilonians for studying strongly correlated systems, such as quantum spin systems. After defining local relevant degrees of freedom, the numerical Contractor Renormalization (CORE) method is applied in two steps: (i) building an effective Hamiltonian with longer ranged interactions up to a certain cut-off using the CORE algorithm and (ii) solving this new model numerically on finite clusters by exact diagonalization and performing finite-size extrapolations to obtain results in the thermodynamic limit. This approach, giving complementary information to analytical treatments of the CORE Hamiltonian, can be used as a semi-quantitative numerical method to study frustrated magnets (as the S=1/2 kagome lattice) or doped systems.