perturbation series could be summed then the correlation function naturally would not contain any fitting parameter.

Ground state fidelity susceptibility at the Berezinskii-Kosterlitz-Thouless quantum phase transition
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In quantum many-body systems, at zero temperature, phase transitions can be encountered when changing strength $\lambda$ of the certain term in the Hamiltonian, $\hat{H}=\hat{H}_{0}+\lambda \hat{V}$. In the finite-size computational studies, a quantity that can be sensitive to the rapid change of the ground state is the overlap of two ground states at slightly different values of the parameter $\lambda$, $F(\lambda,\lambda+\delta\lambda)=\langle \psi_0(\lambda)|\psi_0(\lambda+\delta\lambda)\rangle$ [@ZanardiPaunkovic06] and is called a ground-state fidelity. The ground-state fidelity susceptibility per site (FS) [@You+07; @ZanardiGiordaCozzini07; @VenutiZanardi07] is defined as $$\label{FS1}
\chi_{L}=(1/L)\lim_{\delta\lambda\to0} \big[-2\ln
|F(\lambda,\lambda+\delta\lambda)|\big]/(\delta\lambda)^{2}$$ and is expected to diverge in the thermodynamic limit at certain quantum phase transitions.

Calculating numerically FS has been established as an unbiased indicator of quantum phase transitions [@Schwandt+09; @Gu10rev], especially in one-dimensional systems where a highly accurate numerical calculation of the ground state wave function is possible due to the well established methods, such as DMRG.

Another attractive feature of FS is that even though it can be computed solely from the ground-state wave functions, it contains information about the matrix element of operator $\hat V$ between 