Fractional excitations in low-dimensional spin systems [Elektronische Ressource] / von Ronny Thomale

Description

Fractional Excitations inlow–dimensional spin systemsZur Erlangung des akademischen Grades einesDOKTORS DER NATURWISSENSCHAFTENvon der Fakult¨at fu¨r Physik derUniversit¨at (TH) KarlsruhegenehmigteDISSERTATIONvonDipl.-Phys. Ronny Thomaleaus Mu¨nsterReferent: Prof. Dr. Peter W¨olfle, TKMKorreferent: Prof. Dr. Alexander Mirlin, INTDatum der Pru¨fung: 21. November 2008AcknowledgmentsQui dedit beneficium, taceat. Narret, qui accepit.–LuciusAnnaeusSenecaIt is hard to say in words how much I thank my advisor Martin Greiter.Since my first semester at University, he provided me help, advice, and guid-ance to find and subsequently follow the path of theoretical physics. Withgenerosityandpatiencehedidnotonlyteachmehowtothinkaboutphysics,but most importantly also how to live with it.I am grateful to Peter W¨olfle for his constant support and for giving methe opportunity to do this thesis at the Institut fu¨r Theorie der Konden-sierten Materie (TKM). I also thank Alexander Mirlin for taking over theco-refereeing of my thesis.I thank the Studienstiftung des deutschen Volkes forthe PhD scholarshipby which my work was predominantly financed.There aremanypeopleIhavebeendiscussing andworkingwithwhogaveme a lot of support and provided me important insights into various fieldsof physics. I especially wish to thank Bogdan A.

Sujets

• Physik

Informations

• Publié par: karlsruher_institut_fur_technologie
• Publié le: 01 janvier 2008
• Nombre de lectures: 14
• Langue: English

Extrait

FractionalExcitationsin
low–dimensionalspinsystems

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voUnndiverersFiatka¨tul(ta¨TtHf)u¨rKParhlysrsiukheder

genehmigte

DISSERTATION

nov

Dipl.-Phys.RonnyThomale
ausMu¨nster

Referent:Prof.Dr.PeterWo¨le,TKM
Korreferent:Prof.Dr.AlexanderMirlin,INT
DatumderPru¨fung:21.November2008

Acknowledgments

Quideditbenecium,taceat.Narret,quiaccepit.

–LuciusAnnaeusSeneca
ItishardtosayinwordshowmuchIthankmyadvisorMartinGreiter.
SincemyrstsemesteratUniversity,heprovidedmehelp,advice,andguid-
ancetondandsubsequentlyfollowthepathoftheoreticalphysics.With
generosityandpatiencehedidnotonlyteachmehowtothinkaboutphysics,
butmostimportantlyalsohowtolivewithit.
IamgratefultoPeterWo¨leforhisconstantsupportandforgivingme
theopportunitytodothisthesisattheInstitutfu¨rTheoriederKonden-
siertenMaterie(TKM).IalsothankAlexanderMirlinfortakingoverthe
co-refereeingofmythesis.
IthanktheStudienstiftungdesdeutschenVolkesforthePhDscholarship
bywhichmyworkwaspredominantlynanced.
TherearemanypeopleIhavebeendiscussingandworkingwithwhogave
mealotofsupportandprovidedmeimportantinsightsintovariouselds
ofphysics.IespeciallywishtothankBogdanA.Bernevig,UlfBissbort,
SebastienDusuel,MaxFu¨hringer,MasudulHaque,WalterHofstetter,Eliot
Kapit,FransKlinkhamer,MarcusKollar,Dung-HaiLee,KaiP.Schmidt,
PeterSchmitteckert,UliSchollwo¨ck,DarrellF.Schroeter,DirkSchuricht,
AlexanderSeidel,JulienVidal,MatthiasVojta,aswellasallparticipantsof
theLXXXIXLesHouchesSummerSchoolonexactmethodsinoneandtwo
dimensions.Inparticular,IthankmycolleagueStephanRachelforendless
discussionsaboutandbeyondphysics,andhisfriendship.
IthankallmembersoftheTKMIhavehadthefavortospendtime
withinKarlsruhe.Inparticular,IwishtomentionLarsFritz,StefanKre-
mer,JohannesReuther,BurkhardScharfenberger,HolgerSchmidt,Alexan-
derSchu¨ssler,TobiasUlbricht,andoursecretaryRoseSchrempp.

WithinthetimeperiodofthePhD,manysituationshavearisedIcould
nothavehandledwithoutmybestfriendMatthias,mybrotherChris,my
motherUrsula,andMonika.
Finally,IthankmybelovedfatherEckhard-foreverythingandalltime.

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Thomale

Listofpublications

1.E.Kapit,R.Thomale,D.F.Schroeter,andM.Greiter,ParentHamil-
tonianfortheChiralSpinLiquid,submittedtoPhys.Rev.B.
2.M.GreiterandR.Thomale,Non-Abelianstatisticsinaquantumanti-
ferromagnet,submittedtoPhys.Rev.Lett.
3.M.Fu¨hringer,S.Rachel,R.Thomale,M.Greiter,andP.Schmitteckert,
DMRGstudiesofcriticalSU(n)spinchains,toappearinAnnalsof
Physics(Leipzig).
4.R.ThomaleandM.Greiter,Numericalanalysisofthree-bandmod-
elsforCuOplanesascandidatesforaspontaneousTviolatingorbital
currentphase,Phys.Rev.B77,094511(2008).
5.D.F.Schroeter,E.Kapit,R.Thomale,andM.Greiter,SpinHamilto-
nianforwhichtheChiralSpinLiquidistheExactGroundState,
Phys.Rev.Lett.99,097202(2007).
6.M.GreiterandR.Thomale,Noevidenceforspontaneouscurrentsin
nitesizestudiesofthree-bandmodelsforCuOplanes,
Phys.Rev.Lett.99,027005(2007).
7.R.Thomale,D.Schuricht,andM.Greiter,ChargeexcitationsinSU(n)
spinchains:exactresultsforthe1/r2model,
Phys.Rev.B75,02445(2007).
8.R.Thomale,D.Schuricht,andM.Greiter,Exacttwo-holonwavefunc-
tionsintheKuramoto–Yokoyamamodel,
Phys.Rev.B74,024423(2006).

Contents

1Introduction

31

2Holonexcitationsinantiferromagneticspinchains19
2.1Introduction............................19
2.2Kuramoto–Yokoyamamodel...................20
2.3Vacuumstate...........................21
2.4Spinonexcitations........................22
2.5One-Holonexcitations......................24
2.6Two-Holonexcitations......................26
2.6.1Momentumeigenstates..................26
2.6.2Energyeigenstates....................26
2.7Statisticalparameter.......................27
2.8SummaryandOutlook......................28

3HolonexcitationsinSU(n)spinchains31
3.1Introduction............................31
3.2SU(3)Kuramoto–Yokoyamamodel...............32
3.2.1Vacuumstate.......................34
3.2.2Coloronexcitations....................35
3.2.3One-Holonexcitations..................37
3.2.4Two-Holonexcitations..................39
3.3GeneralizationtoSU(n).....................41
3.3.1Hamiltonian........................41
3.3.2Vacuumstate.......................42
3.3.3Spinonexcitations....................42
3.3.4One-Holonexcitations..................43
3.3.5Two-Holonexcitations..................44
3.4FractionalStatisticsofholonsinSU(n)spinchains......45
3.5Spin-chargeSeparationofSU(n)Fermions...........46

01

Contents

3.6SummaryandOutlook......................47

4MicroscopicmodelfortheChiralSpinLiquid49
4.1Introduction............................49
4.2ChiralSpinLiquidstate.....................51
4.2.1FromtheHaldane–ShastrychaintotheChiralSpin
Liquid...........................51
4.2.2Chiralspinliquidwavefunctiononthetorus......52
4.2.3Spinonwavefunctions..................53
4.2.4GenerationfromlledLandaulevels..........54
4.2.5Holonexcitations.....................55
4.3ConstructionofaParentHamiltonian..............55
4.4Destructionoperators.......................57
4.4.1Vectordestructionoperator...............58
4.4.2Tensordestructionoperator...............59
4.4.3Coecients........................60
4.5Proof................................61
4.6KernelSweepingMethod.....................61
4.7Numerics.............................63
4.8SummaryandOutlook......................65

5Non-AbelianChiralSpinLiquid67
5.1Introduction............................67
5.2Non-abelianchiralspinliquidstate...............68
5.2.1Singletproperty......................69
5.2.2GenerationfromlledLandaulevels..........70
5.3Non-abelianspinonandholonexcitations............72
5.4Microscopicmodel-HamiltonianFindermethod........72
5.5Generalscopeofnon-Abelianspinons..............75
5.6SummaryandOutlook......................75

6Experimentalobservationoffractionalexcitations77
6.1Introduction............................77
6.2SpinonsandHolonsinonedimension..............78
6.2.1Stateoftheeld.....................78
6.2.2Inuenceoffractionalstatistics.............80
6.3FractionalexcitationsintheQuantumHalleect.......80
6.3.1Stateofthe