Zero-temperature renormalization-group method for quantum systems. II. IsotropicX−Ymodel in a transverse field in one dimension

A zero-temperature real-space renormalization-group method is applied to the one-dimensional quantum spin-½ isotropic $X-Y$ model in a transverse field. A line of unstable fixed points is found and is attributed to the oscillatory behavior of the correlation functions. Magnetization components and critical indices are in good agreement with the exact results. The behavior of the $\mathrm{xx}$ correlation function is studied near the critical field.