Conformal properties of one-dimensional quantum systems with long-range interactions

CARLOS M. NAÓN, MARIANO J. SALVAY, MARTA L. TROBO

PHYSICAL REVIEW B - CONDENSED MATTER AND MATERIALS PHYSICS

APS

Lugar: Nueva York; Año: 2005 vol. 72 p. 245110 - 245115

0163-1829

We investigate conformal properties of a one-dimensional quantum system with a long-range, Coulomb-like potential of the form (1/x)^sigma, with sigma >0. We compute the conformal anomaly c as function of sigma. We obtain c=0 for sigma <1 (Wigner crystal) and c=1 for sigma >1 (Luttinger liquid). By studying the scaling regime of the system when it is deformed by the inclusion of a term t rho(x) (with rho(x) a scaling operator), we show that, for sigma >1, the correlation length xi gets an additional interaction dependent factor. This leads to a necessary redefinition of xi in order to avoid an unphysical dependence of the central charge on the coupling constant.