Bosonic Gaussian states from conformal field theory

TL;DR

This paper explores nonchiral wave functions derived from conformal field theory of a free boson, demonstrating their Gaussian state structure, analyzing entanglement properties, and constructing a related Hamiltonian in 1D and 2D.

Contribution

It introduces a method to treat CFT-derived wave functions as bosonic Gaussian states, enabling efficient analysis of correlations and entanglement in multiple dimensions.

Findings

Entanglement entropy matches CFT predictions in 1D.

Constructed a 1D parent Hamiltonian with free boson spectrum.

Identified edge excitations in 2D entanglement spectrum without topological order.

Abstract

We study nonchiral wave functions for systems with continuous spins obtained from the conformal field theory (CFT) of a free, massless boson. In contrast to the case of discrete spins, these can be treated as bosonic Gaussian states, which allows us to efficiently compute correlations and entanglement properties both in one (1D) and in two spatial dimensions (2D). In 1D, the computed entanglement entropy and spectra are in agreement with the underlying CFT. Furthermore, we construct a 1D parent Hamiltonian with a low-energy spectrum corresponding to that of a free, massless boson. In 2D, we find edge excitations in the entanglement spectrum, although the states do not have intrinsic topological order, as revealed by a determination of the topological entanglement entropy.