The structure of nonchiral topological order:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2011
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| Schlagworte: | |
| Online-Zugang: | kostenfrei https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20110519-1072458-1-9 Inhaltsverzeichnis |
| Beschreibung: | XIII, 129 S. graph. Darst. |
Internformat
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Datensatz im Suchindex
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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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