Extracting critical exponents for sequences of numerical data via series extrapolation techniques

TL;DR

This paper introduces a general method to determine critical exponents from numerical data sequences in quantum lattice models by reformulating data as series expansions, enabling the use of extrapolation techniques to identify critical points and exponents.

Contribution

The paper presents a novel, generic scheme for extracting critical exponents from numerical data sequences using series extrapolation techniques in quantum lattice models.

Findings

Successfully applied to the deconfinement transition of the antiferromagnetic spin 1/2 Heisenberg chain.

Provides a systematic way to determine critical points and exponents from numerical data.

Enhances analysis of non-perturbative quantum models with series extrapolation methods.

Abstract

We describe a generic scheme to extract critical exponents of quantum lattice models from sequences of numerical data which is for example relevant for non-perturbative linked-cluster expansions (NLCEs) or non-pertubative variants of continuous unitary transformations (CUTs). The fundamental idea behind our approach is a reformulation of the numerical data sequences as a series expansion in a pseudo parameter. This allows to utilize standard series expansion extrapolation techniques to extract critical properties like critical points and critical exponents. The approach is illustrated for the deconfinement transition of the antiferromagmetic spin 1/2 Heisenberg chain.