Holographic Superfluid at Zero

ZeroTemperatureHolographicSuperfluid
ChaoNiu (GIST)
basedonarXiv:1601.00257 1602.03824with:
Minyong Guo,Shanquan Lan,YuTianandHongbao Zhang
23Feb2016@KIAS
Outline
• 1.Introductionandmotivation
• 2.Holographicmodel
• 3.LinearResponseTheory
• 4.Non-linearEvolution
• 5.SummaryandOutlook
2
Motivation
Quantumcriticalbehaviorofultracoldcesiumatomsinanopticallattice
Science335,1070(2012)
Introduction:Holographicmodel
Thefive-dimensionalEinstein-Maxwell-scalartheory
Vacuumphase
Superfluidphase
T.Nishioka,S.Ryu,andT.Takayanagi,JHEP1003,131(2010)
Introduction:Holographicmodel
Conductivity
Vacuumphase
Superfluidphase
Ourgoalistofillsomegapsintheprevious
investigationsoftheaboveholographicmodel.
T.Nishioka,S.Ryu,andT.Takayanagi,JHEP1003,131(2010)
Holographicmodel
Action
AdSsolitonasthebulkgeometry
• imposetheperiodicityontotheχcoordinate
• Theinverseofthisperiodicityisusuallyinterpreted
astheconfiningscaleforthedualboundary theory.
Equationsofmotion
Holographicmodel
AsymptoticalbehaviorforthebulkfieldsneartheAdSboundary
withtheaxialgaugeand.
holographicrenormalizedaction
Bytheholographicdictionary
conservedparticlecurrent
condensateorderparameter
BackgroundSolution
Theequationsofmotionforthestaticsolution
Vacuumphase
Superfluidphase
ParticledensityandFreeenergy
LinearResponseTheory
Perturbationbulkfields
Perturbationequations
LinearResponseTheory
Notethatthegaugetransformation
generatesaspurioussolutiontotheaboveperturbationequations
Sucharedundancycanberemovedbyrequiring
attheAdSboundary.
:
Standardquantization
Alternativequantization
Dirichletbc
Neumannbc
OpticalConductivity
decouplesfromtheother
perturbationbulkfields
WithattheAdSboundary,theopticalconductivity
canbeextractedbyholographyas
Vacuumphase
OpticalConductivity
Superfluidphase
Superfluiddensity
Analyticunderstanding:aboosttrick
Superfluiddensity
Boost
AdSsolitonasthebulkgeometry
Then
NormalModes:FrequencyDomainAnalysis
Perturbationbulkfields
Perturbationequations
NormalModes:FrequencyDomainAnalysis
Linearperturbationequations and the boundary conditions
Normalmodes
whichcanbefurtheridentifiedbythedensityplot
NormalModes:TimeDomainAnalysis
Equationsofmotion:Hamiltonformalism
NormalModes:TimeDomainAnalysis
Perturbationequations:
NormalModes:TimeDomainAnalysis
Runge-Kuttamethod
• Thenormalmodescanbeidentifiedbythepeaksinthe
Fouriertransformation oftheevolvingdata.
• Thelocationsarethesameasthosebythefrequency domain
analysiswithournumericalaccuracy.
SoundSpeed
DispersionrelationforthegaplessGoldstone
SoundSpeed
Standardquantization
Alternativequantization
A.Yarom,JHEP0907,070(2009), Phys.Rev.D80,106002(2009)
Non-linearEvolution:Non-thermalization
• Toquenchanequilibriumstateandseewhathappens
• Backreactionofmatterfields
JHEP02,120(2014) Phys.Rev.D90,086004(2014). JHEP12,116(2015)
• Intheprobelimit
X.Gao,A.M.Garca-Garca,H.B.Zeng, and H.Q.Zhang, JHEP06,019(2014)
• Tostartfromanon-equilibriumstateandseehowitevolves
• Hamiltonformalism
• Runge-Kuttamethod
Non-linearEvolution:Non-thermalization
Equationsofmotion:Hamiltonformalism
Non-linearEvolution:Non-thermalization
• Non-thermalization
Summary
• Wemakeuseofthelinearresponsetheorytoworkoutthe
superfluiddensityandsoundspeed.
• Weprovideananalyticprooffortheequalitybetweenthe
superfluiddensityandparticledensity bytheboosttrick.
• Theresultingsoundspeedisfoundtoincreasewiththechemical
potentialandsaturatetothevaluepredictedbyconformalfield
theoryforbothquantizations.
• Weperformafullynon-lineardynamicalevolutionforourzero
temperatureholographicsuperfluidtodemonstratethegeneric
non-thermalization.
Outlook
• Zero Temperature Holographic Periodic Superfluid
Thanksforyourattention!