Revisiting numerical real-space renormalization group for quantum lattice systems

TL;DR

This paper improves the numerical real-space renormalization group method for quantum lattice systems by addressing boundary issues, enabling more accurate low-energy spectrum calculations in 1D and 2D models.

Contribution

It introduces intrinsic prescriptions to correct interblock interactions, overcoming boundary limitations of NRG for lattice systems.

Findings

Successfully applied to 1D Heisenberg antiferromagnet

Effective in 2D tight-binding model

Demonstrates numerical efficiency in low-energy spectra

Abstract

Although substantial progress has been achieved in solving quantum impurity problems, the numerical renormalization group (NRG) method generally performs poorly when applied to quantum lattice systems in a real-space blocking form. The approach was thought to be unpromising for most lattice systems owing to its flaw in dealing with the boundaries of the block. Here the discovery of intrinsic prescriptions to cure interblock interactions is reported which clears up the boundary obstacle and is expected to reopen the application of NRG to quantum lattice systems. While the resulting RG transformation turns out to be strict in the thermodynamic limit, benchmark tests of the algorithm on a one-dimensional Heisenberg antiferromagnet and a two-dimensional tight-binding model demonstrate its numerical efficiency in resolving low-energy spectra for the lattice systems.