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

• URL: http://arxiv.org/abs/2308.01964v1
• Date: Thu, 3 Aug 2023 18:00:04 GMT
• Title: Signature of Criticality in Angular Momentum Resolved Entanglement of Scalar Fields in $d>1$
• Authors: Mrinal Kanti Sarkar, Saranyo Moitra, and Rajdeep Sensarma
• Abstract summary: We show that the scaling of angular momentum resolved entanglement entropy $S_ell$ with the subsystem radius $R$ can clearly distinguish between these states. 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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