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Entanglement entropy of composite Fermi liquid states on the lattice: In support of the Widom formula

Ryan V. Mishmash and Olexei I. Motrunich
Phys. Rev. B 94, 081110(R) – Published 25 August 2016
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Abstract

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: SLd1logL. Using variational Monte Carlo, we calculate the second Rényi entropy for a model wave function of the ν=1/2 composite Fermi liquid (CFL) state defined on the two-dimensional triangular lattice. By carefully studying the scaling of the total Rényi 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 LlogL 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 SLlogL entanglement scaling in such highly entangled gapless phases.

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  • Received 6 June 2016

DOI:https://doi.org/10.1103/PhysRevB.94.081110

©2016 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Ryan V. Mishmash and Olexei I. Motrunich

  • Department of Physics, Institute for Quantum Information and Matter, and Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA

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Issue

Vol. 94, Iss. 8 — 15 August 2016

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