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Entanglement area law from specific heat capacity

Brandão, Fernando G. S. L. and Cramer, Marcus (2015) Entanglement area law from specific heat capacity. Physical Review B, 92 (11). Art. No. 115134. ISSN 1098-0121. doi:10.1103/PhysRevB.92.115134.

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We study the scaling of entanglement in low-energy states of quantum many-body models on lattices of arbitrary dimensions. We allow for unbounded Hamiltonians such that systems with bosonic degrees of freedom are included. We show that, if at low enough temperatures the specific heat capacity of the model decays exponentially with inverse temperature, the entanglement in every low-energy state satisfies an area law (with a logarithmic correction). This behavior of the heat capacity is typically observed in gapped systems. Assuming merely that the low-temperature specific heat decays polynomially with temperature, we find a subvolume scaling of entanglement. Our results give experimentally verifiable conditions for area laws, show that they are a generic property of low-energy states of matter, and constitute proof of an area law for unbounded Hamiltonians beyond those that are integrable.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Brandão, Fernando G. S. L.0000-0003-3866-9378
Additional Information:© 2015 American Physical Society. Received 2 November 2014; revised manuscript received 21 August 2015; published 16 September 2015. We acknowledge support by the EPSRC, the EU Integrated Project SIQS, and the Alexander von Humboldt Foundation through the Alexander von Humboldt Professorship.
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
European Union (EU) Integrated Project SIQSUNSPECIFIED
Alexander von Humboldt FoundationUNSPECIFIED
Issue or Number:11
Classification Code:PACS: 05.30.−d, 03.67.−a, 05.70.−a
Record Number:CaltechAUTHORS:20160607-074448112
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Official Citation:Entanglement area law from specific heat capacity Fernando G. S. L. Brandão and Marcus Cramer Phys. Rev. B 92, 115134
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:67708
Deposited By: Tony Diaz
Deposited On:07 Jun 2016 16:36
Last Modified:11 Nov 2021 03:53

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