Variational Numerical Renormalization Group: Bridging the gap between NRG and Density Matrix Renormalization Group

TL;DR

This paper reformulates the numerical renormalization group as a variational method, enabling systematic improvements and bridging it with the density matrix renormalization group to enhance accuracy in quantum impurity models.

Contribution

It introduces a variational formulation of NRG that allows systematic spectrum improvements and integrates NRG with DMRG techniques.

Findings

Enhanced accuracy of eigenstates in quantum spin chains.

Improved spectral results in the single impurity Anderson model.

Effective bridging of NRG and DMRG methodologies.

Abstract

The numerical renormalization group (NRG) is rephrased as a variational method with the cost function given by the sum of all the energies of the effective low-energy Hamiltonian. This allows to systematically improve the spectrum obtained by NRG through sweeping. The ensuing algorithm has a lot of similarities to the density matrix renormalization group (DMRG) when targeting many states, and this synergy of NRG and DMRG combines the best of both worlds and extends their applicability. We illustrate this approach with simulations of a quantum spin chain and a single impurity Anderson model (SIAM) where the accuracy of the effective eigenstates is greatly enhanced as compared to the NRG, especially in the transition to the continuum limit.