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A Numerical Renormalization Group for Continuum One Dimensional Systems

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I 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 Wilson’s numerical renormalization group with Zamolodchikov’s truncated conformal spectrum approach. The 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. Furthermore the method is sufficiently flexible that it can be extended to the study of arrays of coupled one dimensional systems through a density matrix renormalization group procedure. To demonstrate the approach, I presents results on the spectrum and correlation functions of single quantum Ising chains and coupled arrays thereof. I will also present some preliminary results of single semiconducting carbon nanotubes.

This talk is part of the Irregular seminars in TCM series.

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