A model wavefunction for the composite Fermi liquid: its geometry and entanglement

Kyung-Soo Yi, J. J. Quinn

Scott Geraedts, Jie Wang, F. D. M. Haldane

Piotr Sitko, Seongjoon Yi, J. J. Quinn

Jie Wang

Cristian Voinea, Songyang Pu, Ajit Coimbatore Balram +1 more

The composite fermion Fermi liquid (CFL) state at ν = 1 / 2 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 ν = 1 / 2 [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 S 2 for the CFL variational wave function, we show that the entanglement enhancement is present not only at ν = 1 / 2 , but also at ν = 1 / 4 , as well as in bosonic CFL states at ν = 1 and ν = 1 / 3 fillings. In all cases, we find the scaling of S 2 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.

Ryan V. Mishmash, Olexei I. Motrunich

Quantum phases characterized by surfaces of gapless excitations are known to violate the otherwise ubiquitous boundary law of entanglement entropy in the form of a multiplicative log correction: $S\ensuremath{\sim}{L}^{d\ensuremath{-}1}logL$. Using variational Monte Carlo, we calculate the second R\'enyi entropy for a model wave function of the $\ensuremath{\nu}=1/2$ composite Fermi liquid (CFL) state defined on the two-dimensional triangular lattice. By carefully studying the scaling of the total R\'enyi entropy and, crucially, its contributions from the modulus and sign of the wave function on various finite-size geometries, we argue that the prefactor of the leading $L\phantom{\rule{0.16em}{0ex}}logL$ term is equivalent to that in the analogous free fermion wave function. In contrast to the recent results of Shao et al. [Phys. Rev. Lett. 114, 206402 (2015)], we thus conclude that the ``Widom formula'' holds even in this non-Fermi liquid CFL state. More generally, our results further elucidate---and place on a more quantitative footing---the relationship between nontrivial wave function sign structure and $S\ensuremath{\sim}L\phantom{\rule{0.16em}{0ex}}logL$ entanglement scaling in such highly entangled gapless phases.