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

[摘要] We investigate conformal properties of a one-dimensional quantum system with a long-range, Coulomb-like potential of the form 1/parallel to x parallel to(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.

[发布日期] 2005-12-01

[关键词] MANY-BODY PROBLEM;LUTTINGER-LIQUID BEHAVIOR;CRITICAL EXPONENTS;HEISENBERG CHAIN;THIRRING MODEL;CENTRAL CHARGE;GROUND-STATE;INVARIANCE;TRANSITION;AMPLITUDES