Entanglement scaling and charge fluctuations in a Fermi liquid of composite fermions

The composite fermion Fermi liquid (CFL) state at <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>ν</a:mi><a:mo>=</a:mo><a:mn>1</a:mn><a:mo>/</a:mo><a:mn>2</a:mn></a:mrow></a:math> filling of a Landau level is a paradigmatic non-Fermi liquid borne out purely by Coulomb interactions. But in what ways is this exotic state of matter different from a Fermi liquid? The CFL entanglement entropy was indeed found to exhibit a significant enhancement compared to free electrons [J. Shao , ], which was subsequently ruled out as a finite-size effect by the study of a lattice CFL analog [R. V. Mishmash and O. I. Motrunich, ]. Moreover, the enhancement was not observed in a quasi-one-dimensional limit of the Coulomb ground state at <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>ν</b:mi><b:mo>=</b:mo><b:mn>1</b:mn><b:mo>/</b:mo><b:mn>2</b:mn></b:mrow></b:math> [S. D. Geraedts , ]. Here, we revisit the problem of entanglement scaling in the CFL state realized in a two-dimensional electron gas. Using Monte Carlo evaluation of the second Rényi entropy <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>S</c:mi><c:mn>2</c:mn></c:msub></c:math> for the CFL variational wave function, we show that the entanglement enhancement is present not only at <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>ν</d:mi><d:mo>=</d:mo><d:mn>1</d:mn><d:mo>/</d:mo><d:mn>2</d:mn></d:mrow></d:math>, but also at <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>ν</e:mi><e:mo>=</e:mo><e:mn>1</e:mn><e:mo>/</e:mo><e:mn>4</e:mn></e:mrow></e:math>, as well as in bosonic CFL states at <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mi>ν</f:mi><f:mo>=</f:mo><f:mn>1</f:mn></f:mrow></f:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>ν</g:mi><g:mo>=</g:mo><g:mn>1</g:mn><g:mo>/</g:mo><g:mn>3</g:mn></g:mrow></g:math> fillings. In all cases, we find the scaling of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:msub><h:mi>S</h:mi><h:mn>2</h:mn></h:msub></h:math> with subsystem size to be enhanced compared to the noninteracting case, and insensitive to the choice of geometry and projection to the lowest Landau level. We also demonstrate that for CFL states, the variance of the particle number in a subsystem obeys area-law scaling with a universal subleading corner contribution, in stark contrast with free fermions. Our results establish the enhanced entanglement scaling and suppressed charge fluctuations as fingerprints of non-Fermi-liquid correlations in CFL states.