Scale free property and edge state of Wilson's numerical renormalization group

Abstract

We discuss the scale-free property of Wilson's numerical renormalization group(NRG) for the Kondo impurity problem. The single-particle state of the effective Hamiltonian with a cutoff $\Lambda$ is described by the wavepacket basis having the scale free property; The energy scale of the system can be controlled by the lattice translation of the wavepacket basis with no reference of rescaling of the lattice space. We also analyze the role of the Kondo interaction in the context of wavepacket basis and then discuss the scaling and renormalization of the Kondo coupling. In addition, we clarify the role of the edge state in the lowest energy scale of Wilson NRG.

7 pages, 7 figures, expanded analysis of Kondo interaction is added, to appear in PRB

References in corpus (5)

• The numerical renormalization group method for quantum impurity systems
• A class of quantum many-body states that can be efficiently simulated
• Hyperbolic Deformation on Quantum Lattice Hamiltonians
• Entanglement renormalization and boundary critical phenomena
• Wilson-like real-space renormalization group and low-energy effective spectrum of the XXZ chain in the critical regime

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