How quantum phases on cylinders approach the 2d limit

TL;DR

This paper investigates how quantum phases like superconductors and spin liquids on infinite cylinders approach the two-dimensional limit as the cylinder width increases, aiding the interpretation of DMRG results.

Contribution

It analyzes methods to reliably extrapolate finite-cylinder DMRG results to the 2d limit for quantum phases of matter.

Findings

Different extrapolation techniques are compared.

Guidelines for interpreting small-width DMRG results are provided.

Insights into the approach to 2d limit for various quantum phases.

Abstract

We consider the properties of $T=0$ quantum phases of matter - especially superconducting and analogous spin-liquid phases - on infinite cylinders of width $L_\perp$ and analyze the ways in which the $L_\perp \to \infty$ (2d) limit is approached. This problem is interesting in its own right, but is particularly important in the context of extrapolating accessible density matrix renormalization group (DMRG) results on model strongly interacting problems to the desired 2d limit. Various methods for drawing firm conclusions about the quantum phases in 2d from relatively small $L_{\perp}$ results are illustrated.