A Numerical Renormalization Group for Continuum One-Dimensional Systems

TL;DR

This paper introduces a novel numerical renormalization group method that combines Wilson's RG with Zamolodchikov's truncated conformal spectrum approach, enabling detailed study of continuum one-dimensional quantum models.

Contribution

It develops a new RG technique applicable to continuum 1D models, leveraging exactly known eigenstates for efficient computation of physical observables.

Findings

Successfully applied to coupled quantum Ising chains spectrum

Analyzed correlation functions in quantum Ising chain with magnetic field

Demonstrated both numerical and analytical study of RG flow

Abstract

We present a renormalization group (RG) procedure which works naturally on a wide class of interacting one-dimension models based on perturbed (possibly strongly) continuum conformal and integrable models. This procedure integrates Kenneth Wilson's numerical renormalization group with Al. B. Zamolodchikov's truncated conformal spectrum approach. Key to the method is that such theories provide a set of completely understood eigenstates for which matrix elements can be exactly computed. In this procedure the RG flow of physical observables can be studied both numerically and analytically. To demonstrate the approach, we study the spectrum of a pair of coupled quantum Ising chains and correlation functions in a single quantum Ising chain in the presence of a magnetic field.