Multi-fractal geometry of finite networks of spins: Nonequilibrium dynamics beyond thermalization and many-body-localization

Bogdan, Paul; Jonckheere, Edmond; Shermer, Sophie

doi:10.1016/j.chaos.2017.07.008

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Multi-fractal geometry of finite networks of spins: Nonequilibrium dynamics beyond thermalization and many-body-localization

Paul Bogdan, Edmond Jonckheere, Sophie Shermer

Chaos, Solitons & Fractals, Volume: 103, Pages: 622 - 631

Swansea University Author: Sophie Shermer

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DOI (Published version): 10.1016/j.chaos.2017.07.008

Abstract

Quantum spin networks overcome the challenges of traditional charge-based electronics by encoding information into spin degrees of freedom. Although beneficial for transmitting information with minimal losses when compared to their charge-based counterparts, the mathematical formalization of the inf...

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Published in:	Chaos, Solitons & Fractals
ISSN:	0960-0779
Published:	Elsevier BV 2017
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa34852
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first_indexed	2017-08-02T04:16:06Z
last_indexed	2020-07-29T12:53:23Z
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spelling	2020-07-29T11:56:19.9029517 v2 34852 2017-08-01 Multi-fractal geometry of finite networks of spins: Nonequilibrium dynamics beyond thermalization and many-body-localization 6ebef22eb31eafc75aedcf5bfe487777 0000-0002-5530-7750 Sophie Shermer Sophie Shermer true false 2017-08-01 SPH Quantum spin networks overcome the challenges of traditional charge-based electronics by encoding information into spin degrees of freedom. Although beneficial for transmitting information with minimal losses when compared to their charge-based counterparts, the mathematical formalization of the information propagation in a spin(tronic) network is challenging due to its complicated scaling properties. In this paper, we propose a fractal geometric approach for unraveling the information-theoretic phenomena of spin chains and rings by abstracting them as weighted graphs, where the vertices correspond to single spin excitation states and the edges represent the information theoretic distance between pair of nodes. The weighted graph exhibits a complex self-similar structure. To quantify this complex behavior, we develop a new box-counting-inspired algorithm which assesses the mono-fractal versus multi-fractal properties of quantum spin networks. Mono- and multi-fractal properties are in the same spirit as, but different from, Eigenstate Thermalization Hypothesis (ETH) and Many-Body Localization (MBL), respectively. To demonstrate criticality in finite size systems, we define a thermodynamics inspired framework for describing information propagation and show evidence that some spin chains and rings exhibit an informational phase transition phenomenon, akin to the MBL transition. Journal Article Chaos, Solitons & Fractals 103 622 631 Elsevier BV 0960-0779 Quantum spin networks; Information capacity; Fractals; Phase transitions; Nanodevices; Nano-networks; Beyond Turing computation 1 10 2017 2017-10-01 10.1016/j.chaos.2017.07.008 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University 2020-07-29T11:56:19.9029517 2017-08-01T19:16:39.6753176 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Paul Bogdan 1 Edmond Jonckheere 2 Sophie Shermer 0000-0002-5530-7750 3 0034852-01082017191756.pdf fractals-v11.pdf 2017-08-01T19:17:56.4130000 Output 2875809 application/pdf Accepted Manuscript true 2018-07-31T00:00:00.0000000 Released under the terms of a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND). true eng
title	Multi-fractal geometry of finite networks of spins: Nonequilibrium dynamics beyond thermalization and many-body-localization
spellingShingle	Multi-fractal geometry of finite networks of spins: Nonequilibrium dynamics beyond thermalization and many-body-localization Sophie Shermer
title_short	Multi-fractal geometry of finite networks of spins: Nonequilibrium dynamics beyond thermalization and many-body-localization
title_full	Multi-fractal geometry of finite networks of spins: Nonequilibrium dynamics beyond thermalization and many-body-localization
title_fullStr	Multi-fractal geometry of finite networks of spins: Nonequilibrium dynamics beyond thermalization and many-body-localization
title_full_unstemmed	Multi-fractal geometry of finite networks of spins: Nonequilibrium dynamics beyond thermalization and many-body-localization
title_sort	Multi-fractal geometry of finite networks of spins: Nonequilibrium dynamics beyond thermalization and many-body-localization
author_id_str_mv	6ebef22eb31eafc75aedcf5bfe487777
author_id_fullname_str_mv	6ebef22eb31eafc75aedcf5bfe487777_***_Sophie Shermer
author	Sophie Shermer
author2	Paul Bogdan Edmond Jonckheere Sophie Shermer
format	Journal article
container_title	Chaos, Solitons & Fractals
container_volume	103
container_start_page	622
publishDate	2017
institution	Swansea University
issn	0960-0779
doi_str_mv	10.1016/j.chaos.2017.07.008
publisher	Elsevier BV
college_str	Faculty of Science and Engineering
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hierarchy_top_id	facultyofscienceandengineering
hierarchy_top_title	Faculty of Science and Engineering
hierarchy_parent_id	facultyofscienceandengineering
hierarchy_parent_title	Faculty of Science and Engineering
department_str	School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
document_store_str	1
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description	Quantum spin networks overcome the challenges of traditional charge-based electronics by encoding information into spin degrees of freedom. Although beneficial for transmitting information with minimal losses when compared to their charge-based counterparts, the mathematical formalization of the information propagation in a spin(tronic) network is challenging due to its complicated scaling properties. In this paper, we propose a fractal geometric approach for unraveling the information-theoretic phenomena of spin chains and rings by abstracting them as weighted graphs, where the vertices correspond to single spin excitation states and the edges represent the information theoretic distance between pair of nodes. The weighted graph exhibits a complex self-similar structure. To quantify this complex behavior, we develop a new box-counting-inspired algorithm which assesses the mono-fractal versus multi-fractal properties of quantum spin networks. Mono- and multi-fractal properties are in the same spirit as, but different from, Eigenstate Thermalization Hypothesis (ETH) and Many-Body Localization (MBL), respectively. To demonstrate criticality in finite size systems, we define a thermodynamics inspired framework for describing information propagation and show evidence that some spin chains and rings exhibit an informational phase transition phenomenon, akin to the MBL transition.
published_date	2017-10-01T03:43:15Z
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score	11.014067

Multi-fractal geometry of finite networks of spins: Nonequilibrium dynamics beyond thermalization and many-body-localization

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