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We study states of one- and two-dimensional spin systems that are constructedas correlators within the conformal field theory of a massless, free boson. Inone dimension, these are good variational wave functions for XXZ spin chainsand they are similar to lattice Laughlin states in two dimensions. We show thattheir zz correlations are determined by a modification of the originalfree-boson theory. An expansion to quadratic order leads to a solvable,effective theory for the correlations in these states. Compared to the masslessboson, there is an additional term in this effective theory that explains thebehavior of the correlations: a polynomial decay in one dimension and at theedge of a two-dimensional system and an exponential decay in the bulk of atwo-dimensional system. We test the validity of our approximation by comparingit to Monte Carlo computations.

Effective description of correlations for states obtained from conformal field theory