Universität zu Köln

Helmes, Johannes, Stephan, Jean-Marie and Trebst, Simon ORCID: 0000-0002-1479-9736 (2015). Renyi entropy perspective on topological order in classical toric code models. Phys. Rev. B, 92 (12). COLLEGE PK: AMER PHYSICAL SOC. ISSN 1550-235X

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Abstract

Concepts of information theory are increasingly used to characterize collective phenomena in condensed matter systems, such as the use of entanglement entropies to identify emergent topological order in interacting quantum many-body systems. Here, we employ classical variants of these concepts, in particular Renyi entropies and their associated mutual information, to identify topological order in classical systems. Like for their quantum counterparts, the presence of topological order can be identified in such classical systems via a universal, subleading contribution to the prevalent volume and boundary laws of the classical Renyi entropies. We demonstrate that an additional subleading O(1) contribution generically arises for all Renyi entropies S-(n) with n >= 2 when driving the system towards a phase transition, e.g., into a conventionally ordered phase. This additional subleading term, which we dub connectivity contribution, tracks back to partial subsystem ordering and is proportional to the number of connected parts in a given bipartition. Notably, the Levin-Wen summation scheme, typically used to extract the topological contribution to the Renyi entropies, does not fully eliminate this additional connectivity contribution in this classical context. This indicates that the distillation of topological order from Renyi entropies requires an additional level of scrutiny to distinguish topological from nontopological O(1) contributions. This is also the case for quantum systems, for which we discuss which entropies are sensitive to these connectivity contributions. We showcase these findings by extensive numerical simulations of a classical variant of the toric code model, for which we study the stability of topological order in the presence of a magnetic field and at finite temperatures from a Renyi entropy perspective.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Helmes, Johannes UNSPECIFIED UNSPECIFIED UNSPECIFIED Stephan, Jean-Marie UNSPECIFIED UNSPECIFIED UNSPECIFIED Trebst, Simon UNSPECIFIED orcid.org/0000-0002-1479-9736 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-392698
DOI:	10.1103/PhysRevB.92.125144
Journal or Publication Title:	Phys. Rev. B
Volume:	92
Number:	12
Date:	2015
Publisher:	AMER PHYSICAL SOC
Place of Publication:	COLLEGE PK
ISSN:	1550-235X
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language ENTANGLEMENT ENTROPY; BLACK-HOLES; STATISTICS Multiple languages Materials Science, Multidisciplinary; Physics, Applied; Physics, Condensed Matter Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/39269