Holdings: The structure of nonchiral topological order

The structure of nonchiral topological order:

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Bibliographic Details
Main Author:	Buerschaper, Oliver (Author)
Format:	Thesis Book
Language:	English
Published:	2011
Subjects:	Topologische Quantenfeldtheorie Phase > Thermodynamik Hochschulschrift
Online Access:	Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20110519-1072458-1-9 Inhaltsverzeichnis
Physical Description:	XIII, 129 S. graph. Darst.

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MARC


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adam_text	IMAGE 1 TECHNISCHE UNIVERSITAET MUENCHEN MAX-PLANCK-INSTITUT FUER QUANTENOPTIK THE STRUCTURE OF NONCHIRAL TOPOLOGICAL ORDER GERD OLIVER BUERSCHAPER VOLLSTAENDIGER ABDRUCK DER VON DER FAKULTAET FUER PHYSIK DER TECHNISCHEN UNIVERSITAET MUENCHEN ZUR ERLANGUNG DES AKADEMISCHEN GRADES EINES DOKTORS DER NATURWISSENSCHAFTEN (DR. RER. NAT.) GENEHMIGTEN DISSERTATION. VORSITZENDER: UNIV.-PROF. DR. GERHARD ABSTREITER PRUEFER DER DISSERTATION: 1. HON.-PROF. J. IGNACIO CLRAC, PH. D. 2. UNIV.-PROF. DR. WOLFRAM WEISE DIE DISSERTATION WURDE AM 28.04.2011 BEI DER TECHNISCHEN UNIVERSITAET MUENCHEN EINGEREICHT UND DURCH DIE FAKULTAET FUER PHYSIK AM 17.05.2011 ANGENOMMEN. 2011 B 21 193 BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/101424319X DIGITALISIERT DURCH IMAGE 2 CONTENTS 1 INTRODUCTION 1 1.1 TOPOLOGICAL ORDER 1 1.2 QUANTUM DOUBLE MODELS FROM FINITE GROUPS 4 1.3 STRING-NET MODELS 6 1.4 READING GUIDE 10 2 TENSOR NETWORK STATES FOR STRING-NET MODELS 11 2.1 GROUND STATES FROM THE FAT LATTICE 11 2.2 TENSOR NETWORK REPRESENTATIONS 15 2.3 DISCUSSION 17 3 QUANTUM DOUBLE STRING-NET DUALITY 19 3.1 REVISITING STRING-NET MODELS 19 3.2 FOURIER BASIS AND PHYSICAL SUBSPACE 20 3.3 FACE PROJECTORS AND IDENTIFICATION 23 3.4 DISCUSSION 27 4 QUANTUM DOUBLE MODELS FROM HOPF ALGEBRAS 29 4.1 THE LANGUAGE OF HOPF ALGEBRAS 29 4.1.1 HOPF ALGEBRAS 29 4.1.2 QUANTUM DOUBLES AS BICROSSED PRODUCTS 32 4.1.3 HOPF -ALGEBRAS 33 4.2 CONSTRUCTING QUANTUM DOUBLE MODELS FROM HOPF ALGEBRAS 34 4.2.1 GRAPH REPRESENTATIONS OF QUANTUM DOUBLES 35 4.2.2 HILBERT SPACE 47 4.2.3 HAMILTONIAN 49 4.3 DISCUSSION 51 5 HIERARCHY OF HOPF TENSOR NETWORK STATES 53 5.1 DIAGRAMMATIC CALCULUS 56 5.1.1 TENSOR TRACES 56 5.1.2 QUANTUM STATES 63 5.1.3 HIERARCHY 68 5.1.4 PEPS 71 5.2 CALCULATING THE TOPOLOGICAL ENTANGLEMENT ENTROPY 73 5.2.1 ISOMETRIES 74 5.2.2 TRANSFORMING HIERARCHY STATES 82 5.2.3 ENTANGLEMENT ENTROPY 86 XI IMAGE 3 CONTENTS 5.2.4 BOUNDARY CONFIGURATIONS 90 5.3 DISCUSSION 91 6 ELECTRIC-MAGNETIC DUALITY 93 6.1 TORIC CODE AND SELF-DUALITY 93 6.2 REVISITING QUANTUM DOUBLE MODELS 95 6.3 ELECTRIC-MAGNETIC DUALITY 97 6.4 NET OF DUALITIES 99 6.5 TOPOLOGICAL INVARIANTS FROM TENSOR NETWORK STATES 100 6.6 DISCUSSION 102 A PAT LATTICE REDUCTION 103 B CLASSICAL .F-SYMBOLS FROM 3J-SYMBOLS 107 C TRIVIAL HOPF ALGEBRAS AND THEIR QUANTUM DOUBLES 109 C.I TRIVIAL HOPF ALGEBRAS 109 C.2 QUANTUM DOUBLES OF TRIVIAL HOPF ALGEBRAS 110 C.3 HOPF SUBALGEBRAS OF TRIVIAL HOPF ALGEBRAS I LL D AN EXAMPLE OF A NONTRIVIAL FINITE-DIMENSIONAL HOPF C-ALGEBRA 113 D.I THE HOPF ALGEBRA H 8 113 D.2 HOPF SUBALGEBRAS OF H A AND ITS DUAL 114 E HOPF SINGLETS 117 F PROOF OF THEOREM 7 121 XN
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spelling	Buerschaper, Oliver Verfasser aut The structure of nonchiral topological order Gerd Oliver Buerschaper 2011 XIII, 129 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2011 Topologische Quantenfeldtheorie (DE-588)4426450-1 gnd rswk-swf Phase Thermodynamik (DE-588)4263270-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Phase Thermodynamik (DE-588)4263270-5 s Topologische Quantenfeldtheorie (DE-588)4426450-1 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:91-diss-20110519-1072458-1-9 http://mediatum.ub.tum.de/node?id=1072458 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20110519-1072458-1-9 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024158881&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Buerschaper, Oliver The structure of nonchiral topological order Topologische Quantenfeldtheorie (DE-588)4426450-1 gnd Phase Thermodynamik (DE-588)4263270-5 gnd
subject_GND	(DE-588)4426450-1 (DE-588)4263270-5 (DE-588)4113937-9
title	The structure of nonchiral topological order
title_auth	The structure of nonchiral topological order
title_exact_search	The structure of nonchiral topological order
title_full	The structure of nonchiral topological order Gerd Oliver Buerschaper
title_fullStr	The structure of nonchiral topological order Gerd Oliver Buerschaper
title_full_unstemmed	The structure of nonchiral topological order Gerd Oliver Buerschaper
title_short	The structure of nonchiral topological order
title_sort	the structure of nonchiral topological order
topic	Topologische Quantenfeldtheorie (DE-588)4426450-1 gnd Phase Thermodynamik (DE-588)4263270-5 gnd
topic_facet	Topologische Quantenfeldtheorie Phase Thermodynamik Hochschulschrift
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