A Renormalization Group For Treating 2D Coupled Arrays of Continuum 1D Systems

TL;DR

This paper introduces a combined renormalization group and density matrix approach to analyze the spectrum of large 2D arrays of coupled 1D quantum systems, exemplified by quantum Ising chains, capturing phase transitions.

Contribution

It presents a novel hybrid method that effectively studies the spectrum and phase transitions in 2D coupled arrays of continuum 1D systems, especially near critical points.

Findings

Successfully applied to large arrays of quantum Ising chains

Captured the three-dimensional Ising ordering transition

Demonstrated the method's ability across different coupling regimes

Abstract

We study the spectrum of two dimensional coupled arrays of continuum one-dimensional systems by wedding a density matrix renormalization group procedure to a renormalization group improved truncated spectrum approach. To illustrate the approach we study the spectrum of large arrays of coupled quantum Ising chains. We demonstrate explicitly that the method can treat the various regimes of chains, in particular the three dimensional Ising ordering transition the chains undergo as a function of interchain coupling.