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

Mishmash, Ryan V. and Motrunich, Olexei I. (2016) Entanglement entropy of composite Fermi liquid states on the lattice: In support of the Widom formula. Physical Review B, 94 (8). Art. No. 081110. ISSN 2469-9950. doi:10.1103/PhysRevB.94.081110.

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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∼L^(d−1) log L . 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 L log L 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∼L log L entanglement scaling in such highly entangled gapless phases.

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Motrunich, Olexei I.0000-0001-8031-0022
Additional Information:© 2016 American Physical Society. Received 6 June 2016; published 25 August 2016. We gratefully acknowledge Sarang Gopalakrishnan, Hsin-Hua Lai, Max Metlitski, David Mross, Mike Mulligan, Sri Raghu, and Ashvin Vishwanath for valuable discussions. R.V.M. would especially like to thank Jim Garrison for explaining the second Monte Carlo scheme described in the Supplemental Material. This work was supported by the NSF through Grant No. DMR-1206096 (O.I.M.); the Caltech Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with the support of the Gordon and Betty Moore Foundation; and the Walter Burke Institute for Theoretical Physics at Caltech. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant No. ACI-1053575.
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
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Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Issue or Number:8
Record Number:CaltechAUTHORS:20160622-104304294
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Official Citation: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)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:68578
Deposited By: Jacquelyn O'Sullivan
Deposited On:27 Jun 2016 18:04
Last Modified:11 Nov 2021 04:02

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