Signature of Criticality in Angular Momentum Resolved Entanglement of Scalar Fields in $d>1$. arXiv.2308.01964 (2023)

The scaling of entanglement entropy with subsystem size fails to distinguish between gapped and gapless ground state of a scalar field theory in $d>1$ dimensions. We show that the scaling of angular momentum resolved entanglement entropy $S_ell$ with the subsystem radius $R$ can clearly distinguish between these states. For a massless theory with momentum cut-off $Lambda$, $S_ell sim ln [Lambda R/ell]$ for $Lambda R gg ell$, while $S_ell sim R^0$ for the massive theory. In contrast, for a free Fermi gas with Fermi wave vector $k_F$, $S_ell sim ln [k_F R]$ for $k_F R gg ell$. We show how this leads to an ``area-log'' scaling of total entanglement entropy of Fermions, while the extra factor of $ell$ leads to a leading area law even for massless Bosons.