Rapidly-converging methods for the location of quantum critical points from finite-size data

TL;DR

This paper introduces new finite-size scaling methods that rapidly converge to the true quantum critical points, applicable across dimensions and dynamic exponents, demonstrated on spin models including BKT transitions.

Contribution

The authors develop and validate a novel approach for locating quantum critical points with faster convergence than existing methods, using ground-state data from small systems.

Findings

Methods accurately locate quantum critical points.

Faster convergence compared to traditional techniques.

Effective for BKT and other transitions.

Abstract

We analyze in detail, beyond the usual scaling hypothesis, the finite-size convergence of static quantities toward the thermodynamic limit. In this way we are able to obtain sequences of pseudo-critical points which display a faster convergence rate as compared to currently used methods. The approaches are valid in any spatial dimension and for any value of the dynamic exponent. We demonstrate the effectiveness of our methods both analytically on the basis of the one dimensional XY model, and numerically considering c = 1 transitions occurring in non integrable spin models. In particular, we show that these general methods are able to locate precisely the onset of the Berezinskii-Kosterlitz-Thouless transition making only use of ground-state properties on relatively small systems.