Wilson-like real-space renormalization group and low-energy effective spectrum of the XXZ chain in the critical regime

TL;DR

This paper introduces a new real-space renormalization group method for the critical XXZ chain, successfully reproducing the low-energy spectrum and scaling dimensions consistent with Bethe ansatz results.

Contribution

A novel RG approach for the XXZ model that accurately captures low-energy spectra and scaling behavior in the critical regime.

Findings

RG method reproduces Bethe ansatz low-energy spectrum

Proper scaling dimensions are obtained as RG fixed points

Method provides insights into critical behavior of the XXZ chain

Abstract

We present a novel real-space renormalization group(RG) for the one-dimensional XXZ model in the critical regime, reconsidering the role of the cut-off parameter in Wilson's RG for the Kondo impurity problem. We then demonstrate the RG calculation for the XXZ chain with the free boundary. Comparing the hierarchical structure of the obtained low-energy spectrum with the Bethe ansatz result, we find that the proper scaling dimension is reproduced as a fixed point of the RG transformation.