# Effective description of correlations for states obtained from conformal field theory

## TL;DR

This paper develops an effective theory to describe correlations in states derived from conformal field theory, explaining their decay behaviors in one- and two-dimensional spin systems, and validates it with Monte Carlo simulations.

## Contribution

It introduces a quadratic expansion of the free-boson theory to accurately model correlations in conformal field theory-based states, providing analytical insights into their decay properties.

## Key findings

- Effective theory captures polynomial and exponential decay of correlations.
- The approach matches Monte Carlo simulation results.
- Provides a unified framework for 1D and 2D conformal states.

## Abstract

We study states of one- and two-dimensional spin systems that are constructed as correlators within the conformal field theory of a massless, free boson. In one dimension, these are good variational wave functions for XXZ spin chains and they are similar to lattice Laughlin states in two dimensions. We show that their zz correlations are determined by a modification of the original free-boson theory. An expansion to quadratic order leads to a solvable, effective theory for the correlations in these states. Compared to the massless boson, there is an additional term in this effective theory that explains the behavior of the correlations: a polynomial decay in one dimension and at the edge of a two-dimensional system and an exponential decay in the bulk of a two-dimensional system. We test the validity of our approximation by comparing it to Monte Carlo computations.