Application of Contractor Renormalization Group (CORE) to the Heisenberg zig-zag and the Hubbard chain

TL;DR

This paper demonstrates the application of the Contractor Renormalization Group (CORE) method to analyze one-dimensional quantum lattice systems, specifically the Heisenberg zig-zag model and the Hubbard chain, by calculating their ground state energies.

Contribution

It applies the CORE method to 1D quantum systems, showcasing its effectiveness in calculating ground state energies for these models.

Findings

Accurate ground state energy calculations for the Heisenberg zig-zag model.

Successful application of CORE to the Hubbard chain.

Validation of CORE as a useful tool for lattice quantum systems.

Abstract

The COntractor REnormalization group method was devised in 1994 by Morningstar and Weinstein. It was primarily aimed at extracting the physics of lattice quantum field theories (like lattice Quantum Chromodynamics). However, it is a general method of analyzing Hamiltonian lattice systems, e.g. Ising, Heisenberg or Hubbard models. The aim of this work is to show the application of CORE to one-dimensional quantum systems -- the Heisenberg zig-zag model and the Hubbard chain. As a test of the method, the ground state energy of these systems will be calculated.