Signature of Criticality in Angular Momentum Resolved Entanglement of Scalar Fields in $d>1$

TL;DR

This paper demonstrates that angular momentum resolved entanglement entropy scaling can distinguish gapped from gapless scalar fields in higher dimensions, revealing criticality signatures not captured by total entanglement entropy.

Contribution

It introduces angular momentum resolved entanglement entropy as a new diagnostic to identify criticality in scalar fields in dimensions greater than one.

Findings

Massless scalar fields show logarithmic entanglement scaling with subsystem size.

Massive scalar fields exhibit constant entanglement entropy at large scales.

Fermionic systems display a different logarithmic scaling related to the Fermi wave vector.

Abstract

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.