Quantum criticality analysis by finite size scaling and exponential basis sets

TL;DR

This paper introduces a combined finite size scaling and meshfree spectral method using exponential basis sets to accurately analyze quantum criticality, demonstrated on the Hulthen potential with promising convergence and broad applicability.

Contribution

It presents a novel approach integrating finite size scaling with exponential basis sets for quantum criticality analysis, improving accuracy and convergence over traditional methods.

Findings

Method achieves high accuracy in critical parameter estimation.

Converges faster than traditional basis functions.

Applicable to atomic and molecular near-threshold phenomena.

Abstract

We combine the finite size scaling method with the meshfree spectral method to calculate quantum critical parameters for a given Hamiltonian. The basic idea is to expand the exact wave function in a finite exponential basis set and extrapolate the information about system criticality from a finite basis to the infinite basis set limit. The used exponential basis set -though chosen intuitively- allows handling a very wide range of exponential decay rates and calculating multiple eigenvalues simultaneously. As a benchmark system to illustrate the combined approach, we choose the Hulthen potential. The results show that the method is very accurate and converges faster when compared with other basis functions. The approach is general and can be extended to examine near threshold phenomena for atomic and molecular systems based on even-tempered exponential and Gaussian basis functions.