The frustration of being odd: universal area law violation in local systems

Giampaolo, Salvatore Marco; Braga Ramos, F.; Franchini, Fabio (2019) The frustration of being odd: universal area law violation in local systems. Journal of Physics Communications, 3 (8). ISSN 2399-6528

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Official URL: https://iopscience.iop.org/article/10.1088/2399-65...

Abstract

At the core of every frustrated system, one can identify the existence of frustrated rings that are usually interpreted in terms of single–particle physics. We check this point of view through a careful analysis of the entanglement entropy of both models that admit an exact single–particle decomposition of their Hilbert space due to integrability and those for which the latter is supposed to hold only as a low energy approximation. In particular, we study generic spin chains made by an odd number of sites with short-range antiferromagnetic interactions and periodic boundary conditions, thus characterized by a weak, i.e. nonextensive, frustration. While for distances of the order of the correlation length the phenomenology of these chains is similar to that of the non-frustrated cases, we find that correlation functions involving a number of sites scaling like the system size follow different rules. We quantify the long-range correlations through the von Neumann entanglement entropy, finding that indeed it violates the area law, while not diverging with the system size. This behavior is well fitted by a universal law that we derive from the conjectured single–particle picture.

Item Type:

Article

Additional Information:

We thank Andrea Trombettoni, Rosario Fazio, Marcello Dalmonte and Alexander Abanov for useful discussions and Ryan Requist for his careful reading of the first version of the manuscript and his comments. Weare grateful for the computational resources provided by the High Performance Computing Center (NPAD) at UFRN. FF and SMG acknowledge support from the H2020 CSA Twinning project No. 692194, ` RBI-T-WINNING' and from RBI TWINSIN project. FF's work is also partially suppported by the Croatian Science Fund Project No. IP2016-6-3347.

Uncontrolled Keywords:

frustration; entanglement; area law violation

Subjects:

NATURAL SCIENCES > Physics > Condensed Matter Physics

Divisions:

Theoretical Physics Division

Projects:

Project title	Project leader	Project code	Project type
Novel Characterizations of Classical and Quantum Many-Body Systems-ManyBodyCharacteriza	Fabio Franchini	IP-2016-06-3347	HRZZ
Ruđer Bošković Institute: Twinning for a step forward of the Theoretical Physics Division-RBI-T-WINNING	Fabrizio NESTI	692194	EK
Sinergijom do uspjeha: RBI-T-WINNING i ESIF udruženi u jačanju izvrsnosti Zavoda za teorijsku fiziku Instituta Ruđer Bošković-RBI-TWINN-SIN	Blazenka Melic	KK.01.1.1.06.0006	EK