Entanglement entropy of a one-dimensional scalar field

Abstract

In this thesis, we study the entanglement entropy of a chain of coupled harmonic oscillators, which is used to model a one-dimensional bosonic scalar field. Initially, a model for a massless scalar field is discussed. When calculating the entanglement entropy from the reduced density matrix we run into a problem due to the presence of a zero mode, and we are only able to compute the entanglement entropy of one particular case. These difficulties are avoided when we consider a massive scalar field instead, which we accomplish by adding a mass term to the dispersion relation. We numerically study the entanglement entropy of the massive scalar field model as a function of the number of coordinates and the mass parameter and compare with analytical results. By fitting our numerical data we construct a single cross-over function, which describes the entanglement entropy as a function of both the number of coordinates and the mass parameter. The cross-over function agrees well with the numerical data, especially for small values of the mass parameter. Taking then the massless limit, the entanglement entropy of a massless scalar field can nevertheless be determined and reproduces the prediction of conformal field theory.