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We combine the finite size scaling method with the meshfree spectral methodto calculate quantum critical parameters for a given Hamiltonian. The basicidea is to expand the exact wave function in a finite exponential basis set andextrapolate the information about system criticality from a finite basis to theinfinite basis set limit. The used exponential basis set -though chosenintuitively- allows handling a very wide range of exponential decay rates andcalculating multiple eigenvalues simultaneously. As a benchmark system toillustrate the combined approach, we choose the Hulthen potential. The resultsshow that the method is very accurate and converges faster when compared withother basis functions. The approach is general and can be extended to examinenear threshold phenomena for atomic and molecular systems based oneven-tempered exponential and Gaussian basis functions.

Quantum criticality analysis by finite size scaling and exponential basis sets