2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/177320We investigate conformal properties of a one-dimensional quantum system with a long-range, Coulomb-like potential of the form $\frac{1}{|x|^σ}$, with $σ>0$. We compute the conformal anomaly $c$ as function of $σ$. We obtain $c=0$ for $σ<1$ (Wigner crystal) and $c=1$ for $σ>1$ (Luttinger liquid). By studying the scaling regime of the system when it is deformed by the inclusion of a term $t ρ(x)$, (with $ρ(x)$ a scaling operator), we show that, for $σ>1$, the correlation length $ξ$ gets an additional interaction dependent factor. This leads to a necessary redefinition of $ξ$ in order to avoid an unphysical dependence of the central charge on the coupling constant.4 pages, no figures. Sectioning and references added. Content unchanged. To appear in Physical Review BStrongly Correlated ElectronsStatistical MechanicsHigh Energy Physics - Theorytext