Bipartite entanglement properties of squeezed bosons fermions and beyond

Entanglement entropy allows us to quantify long range quantum correlations in topological systems. It is known how to describe the dynamics of coherent states of anyons in quadratic potentials, leading to squeezed states and signatures of fractional statistics. Here, we present an analysis of the entanglement properties of such states as related to the Lowest Landau Level of the quantum Hall bulk. We thus formulate a general method to compute the dynamically evolved Renyi entropies between two anyonic coherent states in the quantum Hall bulk under quadratic potentials. We apply this method to compute the second Renyi entropy between two squeezed coherent states for bosons and for fermions, and pinpoint the effects of quantum statistics. We then describe the application of this method to squeezed coherent states of any fractional statistics. Finally, we discuss how this method may be used to analyze bipartite entanglement of various other topological systems in general.