Mutual Information for Free Fields

Abstract

The entanglement entropy (EE) and mutual information (MI) of spatial regions in general conformal field theories contain universal information which can be used to characterize the corresponding theory. In this study, we perform lattice calculations of these quantities for free scalars and fermions in three spacetime dimensions, which allows us to probe some of these features. In particular, we verify the expected long- and short-distance behaviour of MI in each model, determining the relevant universal coefficients. Based on our results, we conjecture that the leading coefficient in the long-distance expansion of the MI is maximized when the regions are round disks. Additionally, we use the EE of regions with geometric singularities to compute the two-point function stress-tensor coefficient, CT , for a free scalar, obtaining an agreement of ∼ 97% with respect to the exact value