Rahul Nandkishore REGENTS OF THE UNIVERSITY OF COLORADO …

AFRL-AFOSR-VA-TR-2020-0180

Non-equilibrium dynamics and many body localization in ultracold atoms

Rahul NandkishoreREGENTS OF THE UNIVERSITY OF COLORADO

Final Report09/08/2020

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01 Jul 2019 to 30 Jun 20204. TITLE AND SUBTITLENon-equilibrium dynamics and many body localization in ultracold atoms

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6. AUTHOR(S)Rahul Nandkishore

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14. ABSTRACTAFOSR support enabled the completion of twenty five distinct projects, of which twenty are published and five more are underreview. Signature achievements included the demonstration that many body localization can occur in long range interactingsystems (publications 1-3 below), the discovery of a new class of phenomena in quantum dynamics (publications 7-11below), including both localization in translation invariant systems, which is robust to noise, and also (an infinite number of)new subdiffusive hydrodynamic universality classes, and finally the application of this new theoretical understanding toexperiments on ultracold atoms. All goals of the original proposal were met.

15. SUBJECT TERMSmany body localization, non-equilibrium quantum dynamics

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FinalReportforawardFA9550-17-1-0183Projecttitle:“Non-equilibriumdynamicsandmanybodylocalizationinultracoldatoms”

Datescoveredbythisreport:01July2017–30June2020Nameofrecipient:UniversityofColorado

Institution/address:3100MarineStreet,572UCB,Boulder,CO80309-0572NameofPI:RahulNandkishore

Email:[email protected]:303-492-5404

1) Summaryofaccomplishmentsmadeduringthisgrantperiod

AFOSRsupportenabledthecompletionoftwentyfivedistinctprojects,ofwhichtwentyarepublishedandfivemoreareunderreview.Signatureachievementsincludedthedemonstrationthatmanybodylocalizationcanoccurinlongrangeinteractingsystems(publications1-3below),thediscoveryofanewclassofphenomenainquantumdynamics(publications7-11below),includingbothlocalizationintranslationinvariantsystems,whichisrobusttonoise,andalso(aninfinitenumberof)newsubdiffusivehydrodynamicuniversalityclasses,andfinallytheapplicationofthisnewtheoreticalunderstandingtoexperimentsonultracoldatoms.Allgoalsoftheoriginalproposalweremetorexceeded.Adetaileddescriptionofwhatwasaccomplishedisprovidedattheendofthisreport.

2) Archivalpublications

Publishedarticles

1. ManybodylocalizationwithlongrangeinteractionsRahulM.NandkishoreandS.L.Sondhi,Phys.Rev.X7,041021(2017)[SelectedasaresearchhighlightbyNaturePhysics13,1037(2017)]

2. LocalizationofextendedquantumobjectsMichaelPretkoandRahulM.Nandkishore,Phys.Rev.B98,134301(2018)

3. SymmetrybreakingandlocalizationinarandomSchwingermodelwithcommensurationA.A.Akhtar,RahulM.NandkishoreandS.L.Sondhi,Phys.Rev.B98,115109(2018)

4. ACconductivitycrossoverinlocalizedsuperconductorsA.T.Schmitz,MichaelPretkoandRahulM. Nandkishore,Phys.Rev.B98,144203(2018)

5. Quantumdynamicsofdisorderedspinchainswithpower-lawinteractions.A.Safavi-Naini,M.L.Wall,O.L.Acevedo,A.M.ReyandR.M.Nandkishore,Phys.Rev.A99,033610(2019)[Editor’ssuggestions].

6. EmergentphasesoffractonicmatterAbhinavPrem,MichaelPretkoandRahulM.Nandkishore,Phys.Rev.B97,085116(2018)

7. Localizationinfractonicrandomcircuits.ShriyaPai,MichaelPretkoandRahulM.NandkishorePhys.Rev.X,9,021003(2019)Erratum:Phys.Rev.X,9,021003(2019)

8. LocalizationfromHilbertspaceshattering:Fromtheorytophysicalrealizations.VedikaKhemani,MichaelHermeleandRahulNandkishore,Phys.Rev.B101,174204(2020)[Editors’suggestion]


9. Anomaloussubdiffusionfromsubsystemsymmetries.JasonIaconis,SagarVijayandRahulNandkishore,Phys.Rev.B100,214301(2019)

10. Fractonhydrodynamics.AndreyGromov,AndrewLucas,andRahulM.Nandkishore.Phys.Rev.Research2,033124(2020)

11. Quantumentropicself-localizationwithultracoldfermions.M.Mamaev,I.Kimchi,M.A.Perlin,R.M.Nandkishore,andA.M.Rey.Phys.Rev.Lett.123,130402(2019)

12. Dynamicalscarstatesindrivenfractonsystems.ShriyaPaiandMichaelPretko,Phys.Rev.Lett.123,136401(2019)

13. FractonsfromconfinementinonedimensionShriyaPaiandMichaelPretko,Phys.Rev.Research2,013094(2020)

14. EntanglementSpectraofStabilizerCodes:AWindowintoGappedQuantumPhasesofMatter.AlbertT.Schmitz,Sheng-JieHuang,andAbhinavPrem.Phys.Rev.B99,205109(2019).

15. GaugeStructures:FromStabilizerCodestoContinuumModels,AlbertT.Schmitz,AnnalsofPhysics410(2019):167927

16. SymmetricTensorGaugeTheoriesonCurvedSpaces.KevinSlagle,AbhinavPremandMichaelPretko.AnnalsofPhysics410(2019)167910

17. Fractonphasesofmatter.MichaelPretko,XieChenandYizhiYou,Int.J.ofModernPhysicsA,Vol35,No.6,2030003(2020).

18. RemnantsofAndersonlocalizationinpre-thermalizationinducedbywhitenoiseS.Lorenzo,T.Apollaro,G.M.Palma,R.Nandkishore,A.SilvaandJ.Marino,Phys.Rev.B98,054302(2019)

19. Exploringmany-bodylocalisationinopenquantumsystemsviaWegner-Wilsonflows.ShaneP.Kelly,RahulNandkishoreandJamirMarino,Nucl.Phys.B951,114886(2020)

20. ManybodylocalizationproximityeffectsinplatformsofcoupledspinsandbosonsJ.MarinoandR.M.Nandkishore,Phys. Rev. B 97, 054201 (2018)

Articlessubmittedandunderreview,currentlyavailableinpreprintformonthearXiv

1. ThermalizationanditsabsencewithinKrylovsubspacesofaconstrainedHamiltonian.SanjayMoudgalya,AbhinavPrem,RahulNandkishore,NicolasRegnault,B.AndreiBernevig.arXiv:1910.14048

2. Fractonsfrompolaronsandhole-dopedantiferromagnets:Microscopicrealizations.JohnSousandMichaelPretko,arXiv:1904.08424

3. DistillingFractonsfromLayeredSubsystem-SymmetryProtectedPhases.A.T.Schmitz.ArXiv:1910.04765.

4. Thermalstabilityofdynamicalphasetransitionsinhigherdimensionalstabilizercodes.A.T.Schmitz,ArXiV2002.11733

5. Disordercontrolledrelaxationina3DHubbardmodelquantumsimulator.W.Morong,S.R.Muleady,I.Kimchi,W.Xu,R.M.Nandkishore,A.M.Rey,B.DeMarco.arXiv:2001.07341

Changeinresearchobjectives:None

ChangeinAFOSRprogrammanager:None

Extensionsgrantedormilestonesslipped:None

Inventionsorpatentdisclosures:None


Detailedsummaryofaccomplishments

Wenowprovideadetailedsummaryofwhatwasaccomplished.Theseprojectscanbegroupedintothreedistinctthemes(followingtheoriginalgrantproposal).

A. Non-equilibriumdynamicsandmanybodylocalizationwithlongrangeinteractions

Recentdevelopmentsintheunderstandingofmanybodyquantumdynamicsandmanybodylocalization(MBL)havefocusedonsystemswithinteractionsthatareshortrangeinrealspace.However,many`real’systems(ofcharges,dipoles,etc)exhibitinteractionsthatarelongrangedinrealspace.Thequantumdynamicsoflongrangeinteractingmanybodyquantumsystemsisthusanimportantopenfrontierforresearch,andwasakeythemeofmygrantproposal.

Overthecourseofthegrantperiodwemademajorprogressonthisfront,thankstoAFOSRsupport.Thisprogresscameintheformoffivecompletedandpublishedprojectsthataredescribedbelow.

(i) ManybodylocalizationwithlongrangeinteractionsRahulM.NandkishoreandS.L.Sondhi,Phys.Rev.X7,041021(2017)

Many-bodylocalization(MBL)hasemergedasapowerfulparadigmforunderstandingnon-equilibriumquantumdynamics.FolklorebasedonperturbativeargumentsholdsthatMBLarisesonlyinsystemswithshort-rangeinteractions.Inthiswork,supportedbyAFOSR,weadvancenonperturbativeargumentsindicatingthatMBLcanariseinsystemswithlong-range(Coulomb)interactions,throughamechanismwedub“orderenabledlocalization.”Inparticular,weshowusingbosonizationthatMBLcanariseinone-dimensionalsystemswith∼rinteractions,aproblemthatexhibitschargeconfinement.Wealsoarguethat(throughtheAnderson-Higgsmechanism)MBLcanariseintwo-dimensionalsystemswithlog(r)interactions,andspeculatethatourargumentsmayevenextendtothree-dimensionalsystemswith1/rinteractions.OurargumentsopenedthedoortoinvestigationofMBLphysicsinawidearrayoflong-rangeinteractingsystemswheresuchphysicswaspreviouslybelievednottoarise.

ThisworkwaspublishedinPhysicalReviewX[Phys.Rev.X7,041021(2017)],andwasselectedasaresearchhighlightbyNaturePhysics[NaturePhysics13,1037(2017)]

(ii) LocalizationofextendedquantumobjectsMichaelPretkoandRahulM.Nandkishore,Phys.Rev.B98,134301(2018)

Aquantumsystemofparticlescanexistinalocalizedphase,exhibitingergodicitybreakingandmaintainingforeveralocalmemoryofitsinitialconditions.Inthiswork,supportedbyAFOSR,wegeneralizedthisconcepttoasystemofextendedobjects,suchasstringsandmembranes,arguingthatsuchasystemcanalsoexhibitlocalizationinthepresenceofsufficientlystrongdisorder(randomness)intheHamiltonian.Thisworkextendsthenotionoflocalization(andlocalizationprotectedorder)toahostofsettingswheresuchideaspreviouslydidnotapply.


Importantly,thisworkalsoallowsustodemonstratelocalizationinthreedimensionalsystemswith1/r(Coulomb)interactions–aresultwithobviousexperimentalrelevance.Wepredicttheexistenceofanew`localizedsuperconductor’phaseinwhichlocalizationofquantumfluxlinescouldstabilizesuperconductivityatenergydensitieswhereanormalstatewouldariseinthermalequilibrium.Thiscouldhavesignificanttechnologicalapplications.

Thisworkispublished.Itintroducedthenotionof`MBLsuperconductors.’

(iii) SymmetrybreakingandlocalizationinarandomSchwingermodelwith

commensurationA.A.Akhtar,RahulM.NandkishoreandS.L.Sondhi,Phys.Rev.B98,115109(2018)

Inthisworkwesubjectthescenarioofmanybodylocalizationwithlong-rangeinteractionstostringentnumericaltestsusingbothexactdiagonalizationanddensitymatrixrenormalizationgrouptechniques.Specifically,wefocusontheonedimensionalrealizationoftheseideas(`Schwingermodel’)–whichcanbeaccessedexperimentallyusingtrappedions[seee.g.Nature534,516(2016)].Wenumericallyinvestigatetheinterplayofconfinement,latticecommensuration,anddisorder,intheformofarandomchemicalpotential.Acarefulexaminationofthestructureoflowlyingexcitedstatesrevealsdisorderinducedlocalization,consistentwiththeanalyticexpectationsfromthePI’searliergrantfundedworkPhys.Rev.X7,041021(2017).

Thisworkispublished.

(iv) ACconductivitycrossoverinlocalizedsuperconductorsA.T.Schmitz,MichaelPretkoandRahulM.Nandkishore,Phys.Rev.B98,144203(2018)

In(i)aboveweintroducedthenotionofa`localizedsuperconductor’phaseforthreedimensionalsystemswitha1/rinteraction.Inthisworkwediscusshowsuchaphasemaybeexperimentallycharacterizedusingopticalconductivitymeasurements.Inlocalizedphasesthelow-frequencyACconductivitytypicallyvanishesasωφ.Theexponentφ=2forAndersoninsulators,whereasformanybodylocalizedinsulatorsφisacontinuouslyvaryingexponent1≤φ≤2.Inthiswork,weshowthatinlocalizedsuperconductors,theexponentφcanbemarkedlydifferentfromthecharacteristicvalueforlocalizedinsulators.Thisdifferenceoccursduetosingularitiesinthelow-energydensityofstates,permittedbytheeffectiveparticle-holesymmetryaroundtheFermilevel.Inparticular,incertainsymmetryclassesatzerotemperature,weobtainφ>2.WefurtheridentifyaninterestingtemperaturedependentcrossoverinthescalingformoftheACconductivity,whichcouldbeusefulfortheexperimentalcharacterizationoflocalizedsuperconductors.


(v) Quantumdynamicsofdisorderedspinchainswithpower-lawinteractions.A.Safavi-Naini,M.L.Wall,O.L.Acevedo,A.M.ReyandR.M.Nandkishore,Phys.Rev.A99,033610(2019)[Editor’ssuggestions].

ThisworkextendsthePI’sinvestigationsofMBLinlongrangeinteractingsystemsbeyondthe


previouslyinvestigatedcasesofCoulombinteractions.Inthiswork,wenumericallyinvestigatedthedynamicsofspinchainswithpowerlawlongrangeinteractionsoftunablerange.Specifically,weusedextensivenumericalsimulationsbasedonmatrixproductstatemethodstostudythequantumdynamicsofspinchainswithstrongon-sitedisorderandpower-lawdecaying(1/rα)interactions.Wefocusedontwospin-1=2Hamiltoniansfeaturingpower-lawinteractions:HeisenbergandXY,andcharacterizedtheircorrespondinglong-timedynamicsusingthreedistinctdiagnosticsrelevanttoAMOexperiments:decayofastaggeredmagnetizationpatternI(t),growthofentanglemententropyS(t),andgrowthofquantumFisherinformationFQ(t):Forsufficientlyrapidlydecayinginteractionsα>αcwefoundamany-bodylocalizedphase,inwhichI(t)saturatestoanon-zerovalue,entanglemententropygrowsasS(t)~t1/α,andFisherinformationgrowslogarithmically.Importantly,entanglemententropyandFisherinformationdonotscalethesameway(unlikeshortrangeinteractingmodels).ThecriticalpowerαcissmallerfortheXYmodelthanfortheHeisenbergmodel.Thisworkispublished.

B:Connectionsbetweenquantuminformationtheoryandmanybodydynamics

Asecondthemeofmygrantproposalwasexploringtheconnectionbetweenquantuminformationtheoryandquantumdynamics.Onthisfrontwebenefitedfromastrokeofluck:thediscoveryof`fracton’models,whichsitattheintersectionbetweenquantumdynamicsandquantuminformation.AFOSRsupportenabledustoexplorethepossiblephasesofmatterthatmayariseinsuchmodels.ThisworkwasconductedtogetherwithAbhinavPremandAlbertSchmitz(twograduatestudentspartiallysupportedbythisgrant,bothofwhomgraduatedduringthegrantperiod)andwasreportedinthepublicationslistedbelow.

(vi) Localizationinfractonicrandomcircuits.ShriyaPai,MichaelPretkoandRahulM.NandkishorePhys.Rev.X,9,021003(2019).Erratum:Phys.Rev.X,9,021003(2019)

Inthisworkweintroducedamodelofquantumdynamicssubjecttoconstraints,motivateddirectlybythestudyoffractonsystems.Wenumericallydiscoveredthatthismodelcanexhibitlocalizationeveninthepresenceoftemporalnoise,andintheabsenceofspatialdisorder,unlikeanyothermodeloflocalizationthatweareawareof.Itthusappearstoconstituteaqualitativelynewroutetolocalization.


(vii) LocalizationfromHilbertspaceshattering:Fromtheorytophysicalrealizations.VedikaKhemani,MichaelHermeleandRahulNandkishore,Phys.Rev.B101,174204(2020)[Editors’suggestion]ThisworkcontinuesthestudyofthefractonicrandomcircuitmodelintroducedbythePIin(vi)above,andprovidesacompleteandrigorousanalyticunderstandingofthenewtypeoflocalizationarisingtherein.Specifically,thelocalizationinthismodelisrigorouslyshownasarisingfromaconstraintinduced`shattering’ofHilbertspaceintoahugenumberofdynamicallydistinctsubsectors.This`shattering’phenomenonisshown


toberobust.Illuminatingconnectionsaredrawntoseveralotherareasofconsiderablecurrentinterest,inparticularthestudyof`quantummanybodyscars.’Wealsoexplainhowthephenomenonmaybeextendedtosystemsinarbitraryspatialdimensions,andhowitmayberealizedinneartermultracoldatomexperiments.Thisworkispublished.

(viii) ThermalizationanditsabsencewithinKrylovsubspacesofaconstrainedHamiltonian.SanjayMoudgalya,AbhinavPrem,RahulNandkishore,NicolasRegnault,B.AndreiBernevig.arXiv:1910.14048

Thisworkcontinuesthestudyofconstrainedmodelsoftheformdiscussedinpublications(vi)and(vii)above.Whilethepreviousworksfocusedonthe`localized’(i.e.small)dynamicalsubspacesofthequantumdynamics,thisworkexploredthe`large’subspacesofthequantumdynamics,andwhetherthedynamicsisthermalwithinthese`large’subspaces.Dynamicswithinaparticulardynamicalsubspaceisshowntobethermalforsomesubspaces,butnon-thermalforothers,withthenon-thermalityarisingduetoanunusualformofintegrability,whichbecomesapparentonlywhenthedynamicsisprojectedonaparticulardynamicalsubspace.

ThisworkisunderreviewandiscurrentlyavailableonthearXiv.

(ix) Anomaloussubdiffusionfromsubsystemsymmetries.JasonIaconis,SagarVijayandRahulNandkishore,Phys.Rev.B100,214301(2019)

Inthiswork,weintroducedanewmethodforsimulatingquantumdynamics,whichallowsustoefficientlysimulatetolongtimes`almostchaotic’quantumdynamics.ThisnewmethodisbasedonacombinationofcellularautomatonideasandMonteCarlomethods.Weapplythisnewmethodtosimulatethequantumdynamicsofsystemswith`fracton’likeconstraintsintwoandthreespacedimensionsandnumericallydiscoversubdiffusion.Weanalyticallyexplaintheoriginofthesubdiffusionintheparticularcases.Wealsoarguethattheclassofdynamicssimulableusingournewtechniqueismuchcloserto`generic’chaoticquantumdynamicsthanthekindsofdynamicsthatweresimulablepreviously.

Thisworkispublished

(x) Fractonhydrodynamics.AndreyGromov,AndrewLucas,andRahulM.Nandkishore.Phys.Rev.Research2,033124(2020)

Inthisworkweexaminethebehaviorofconstrainedquantumdynamics(alongthelinesstudiedin(vi)-(viii)above),inthecasewhenthe`non-thermal’regionsofHilbertspacediscussedabove


aremeasurezerointhethermodynamiclimit.Inthiscase,genericinitialconditionsdothermalize,butwearguethattheydosoinsubdiffusivemanner.Weintroducenewclassesofhydrodynamictheoriestodescribethethermalizationofsuchfractonmatter.Eachofthesetheoriesexhibitssubdiffusivethermalization,andconstitutesanewuniversalityclassofhydrodynamicbehavior.Thereareinfinitelymanysuchclasses,eachwithdistinctsubdiffusiveexponents,allofwhicharecapturedbyourformalism.Ourframeworknaturallyexplainsrecentresultsondynamicswithconstrainedquantumcircuits,aswellasrecentexperimentswithultracoldatomsintiltedopticallattices.Weidentifycrispexperimentalsignaturesofthesenovelhydrodynamics,andexplainhowtheymayberealizedinneartermultracoldatomexperiments.


(xi) Quantumentropicself-localizationwithultracoldfermions.M.Mamaev,I.Kimchi,M.A.Perlin,R.M.Nandkishore,andA.M.Rey.Phys.Rev.Lett.123,130402(2019)

Thisworkexaminesamodelofconstrainedquantumdynamicsmotivatedbyexperimentsonatomicclocks,andrevealsittoexhibitanunusualkindoffew-bodylocalization.Thisself-localizationisrevealedtobeof`quantumentropic’origin,asrevealedbyamappingtoannon-interactingAndersonimpuritymodel.UsingtechniquesintroducedbythePIin(vi)above,theresultsareextendedalsotomany-bodysystems,andaconnectionismadetothedynamicsof`Hilbertspacefracture’discussedin(vi)–(viii)above.


(xii) Dynamicalscarstatesindrivenfractonsystems.ShriyaPaiandMichaelPretko,Phys.

Rev.Lett.123,136401(2019)

ThisworkexaminesfractoniccircuitmodelsofthetypeintroducedbythePIin(vi)above,andmakesaconnectionbetweentheirbehaviorandquantumscars.ItdoesnotinvolvethePIasanauthorbutisgrantrelevantandwascarriedoutbyanAFOSRfundedstudentandpostdoc.Thisworkispublished.

(xiii) FractonsfromconfinementinonedimensionShriyaPaiandMichaelPretko,Phys.Rev.

Research2,013094(2020)

Thisworkexplainshow`fracton’constraints,whoseconsequencesareexploredin(vi)-(xii)above,mayariseinonedimensionalconfiningquantumsystems,suchasU(1)gaugetheoryandthequantumIsingmodel.ThisworkdoesnotinvolvethePIasanauthor,butisgrantrelevantandwascarriedoutbyapostdocfundedinpartbyAFOSR.Thisworkispublished.

(xiv) EntanglementSpectraofStabilizerCodes:AWindowintoGappedQuantumPhasesofMatter.AlbertT.Schmitz,Sheng-JieHuang,andAbhinavPrem.Phys.Rev.B99,205109(2019).


Theentanglementspectrum(ES)providesabarometerofquantumentanglementandencodesphysicalinformationbeyondthatcontainedintheentanglemententropy.ThispaperexplorestheESofstabilizercodes,whichfurnishexactlysolvablemodelsforaplethoraofgappedquantumphasesofmatter.Inparticular,itstudiesmodelsharboringfractonorder,andcomparestheresultingESwiththatofbothconventionaltopologicalorderandof(strong)subsystemsymmetryprotectedtopological(SSPT)states.Thisshedsfurtherlightontheinterplaybetweengeometricandtopologicaleffectsinfractonphasesofmatter.Itfurthershowsthataversionoftheedge-entanglementcorrespondence,establishedearlierforgappedtwo-dimensionaltopologicalphases,alsoholdsforgappedthree-dimensionalfractonmodels.

ThisisworkthatdoesnotinvolvethePIasanauthor,butisgrantrelevantandwasledbythePI’sAFOSRfundedstudent.Itispublished.

(xv) GaugeStructures:FromStabilizerCodestoContinuumModels,AlbertT.Schmitz,AnnalsofPhysics410(2019):167927Thispaperdevelopsanewformalperspectivecapableofdescribingfractonphasesofmatter.Itilluminatesthegeneralstructureoffractonphases,aswellashowtheyconnecttocontinuumtheories.ThisisworkthatdoesnotinvolvethePIasanauthor,butisgrantrelevantandwasledbythePI’sAFOSRfundedstudent.Thisworkispublished.

(xvi) SymmetricTensorGaugeTheoriesonCurvedSpaces.KevinSlagle,AbhinavPremandMichaelPretko.AnnalsofPhysics410(2019)167910Fractonsandothersubdimensionalparticlesareanexoticclassofemergentquasi-particleexcitationswithseverelyrestrictedmobility.Awideclassofmodelsfeaturingthesequasi-particleshaveanaturaldescriptioninthelanguageofsymmetrictensorgaugetheories.Thisworkinvestigatesthefateofsymmetrictensorgaugetheoriesinthepresenceofspatialcurvature.Itshowsthatweakcurvaturecaninducesmall(exponentiallysuppressed)violationsonthemobilityrestrictionsofcharges,leavingasenseofasymptoticfractonic/sub-dimensionalbehaviorongenericmanifolds.Nevertheless,certainsymmetrictensorgaugetheoriesmaintainsharpmobilityrestrictionsandgaugeinvarianceoncertainspecialcurvedspaces,suchasEinsteinmanifoldsorspacesofconstantcurvature.

ThisisworkthatdoesnotinvolvethePIasanauthor,butisgrantrelevantandinvolvesthePI’sAFOSRfundedstudent(Prem),whohassincegraduated.Thisworkispublished.

(xvii) EmergentphasesoffractonicmatterAbhinavPrem,MichaelPretkoandRahulM.Nandkishore,Phys.Rev.B97,085116(2018)


Fractonsareemergentparticleswhichareimmobileinisolation,butwhichcanmovetogetherindipolarpairsorothersmallclusters.Theseexoticexcitationsnaturallyoccurincertainquantumphasesofmatterdescribedbytensorgaugetheories.Previousresearchhasfocusedonthepropertiesofsmallnumbersoffractonsandtheirinteractions,effectivelymappingoutthe“standardmodel”offractons.Inthepresentwork,however,weconsidersystemswithafinitedensityofeitherfractonsortheirdipolarboundstates,withafocusontheU(1)fractonmodels.Westudysomeofthephasesinwhichemergentfractonicmattercanexist,therebyinitiatingthestudyofthe“condensedmatter”offractons.Webeginbyconsideringasystemwithafinitedensityoffractons,whichweshowcanexhibitmicroemulsionphysics,inwhichfractonsformsmall-scaleclustersemulsedinaphasedominatedbylong-rangerepulsion.Wethenmoveontostudysystemswithafinitedensityofmobiledipoles,whichhavephasesanalogoustomanyconventionalcondensedmatterphases.Wefocusontwomajorexamples:FermiliquidsandquantumHallphases.AfinitedensityoffermionicdipoleswillformaFermisurfaceandenteraFermiliquidphase.Interestingly,thisdipolarFermiliquidexhibitsafinite-temperaturephasetransition,correspondingtoanunbindingtransitionoffractons.Finally,westudychiraltwo-dimensionalphasescorrespondingtodipolesin“quantumHall”statesoftheiremergentmagneticfield.WestudynumerousaspectsofthesegeneralizedquantumHallsystems,suchastheiredgetheoriesandgroundstatedegeneracies.Thisworkispublished.

(xviii) Fractonsfrompolaronsandhole-dopedantiferromagnets:Microscopicrealizations.JohnSousandMichaelPretko,arXiv:1904.08424

Thisworkshowsthatboson-affectedhoppingmodelscanprovideanaturalrealizationoffractons,eitherapproximatelyorexactly,dependingonthedetailsofthesystem.Itfirstconsidersagenericonedimensionalboson-affectedhoppingmodel,inwhichsingleparticlesmoveonlyatsixthorderinperturbationtheory,whilemotionofboundstatesoccursatsecondorder,allowingforabroadparameterregimeexhibitingapproximatefractonphenomenology.Itthenstudiesaspecialtypeofboson-affectedhoppingmodelswithmutualhard-corerepulsionbetweenparticlesandbosons,accessibleinhole-dopedmixed-dimensionalIsingantiferromagnets,inwhichtheholemotionisonedimensionalinanotherwisetwo-dimensionalantiferromagneticbackground.Thissystem,whichiswithinthecurrentreachofultracold-atomexperiments,exhibitsperfectfractonbehaviortoallordersinperturbationtheory.Diagnosticsignaturesoffractonicbehaviorinthesesystemsarediscussed.Thisworkpresentsboson-affectedhoppingsystemsasanaturalplatformforstudyingimportantaspectsoffractonphysics,suchasrestrictedthermalization.

ThisisworkthatdoesnotinvolvethePIasanauthor,butisgrantrelevantandinvolvesthePI’sAFOSRfundedpostdoc(Pretko).ItisunderreviewandcurrentlyavailableonthearXiv.

(xix) DistillingFractonsfromLayeredSubsystem-SymmetryProtectedPhases.A.T.Schmitz.

ArXiv:1910.04765.


Thispaperexplainshowparadigmatic`fractonmodels’includingtheHaahcubiccodemaybeobtainedviaa`layerconstruction’fromlowerdimensionalphases.Fractonphasesweretheinspirationfortheexplorationsofquantumdynamicsin(vi)–(xvii)above.ThisworkdoesnotinvolvethePIasanauthorbutisgrantrelevantandwascarriedoutbythePI’sAFOSRfundedstudent.

ThisworkispubliclyavailableasapreprintonthearXiv.Thestudent(andsoleauthor)hasgraduatedandmovedtoanindustryjobatIntelCorp.soitislikelythatthiswillremainapreprint.

(xx) Thermalstabilityofdynamicalphasetransitionsinhigherdimensionalstabilizer

codes.A.T.Schmitz,ArXiV2002.11733Thispaperexplainshowdynamicalphasetransitions(i.e.singularitiesintheLoschmidtecho)canbeobtainedindimensionshigherthanone,andatnon-zerotemperature.ThepaperdoesnotinvolvethePIasanauthorbutisgrantrelevantandwascarriedoutbythePIsAFOSRfundedstudent.ThemanuscriptispubliclyavailableasapreprintontheArXiv.Theauthorhassincegraduatedandmovedtoanindustryjob(atIntelcorp).soitseemslikelythiswillremainapreprint.

(xxi) Fractonphasesofmatter.MichaelPretko,XieChenandYizhiYou,Int.J.ofModern

PhysicsA,Vol35,No.6,2030003(2020).InvitedreviewonfractonswrittenbythePI’sAFOSRsupportedpostdoc,Dr.MichaelPretko.

C:Decoherenceoflocalizedsystems

Thefinalthemeofmygrantproposalwasstudyingthedecoherenceoflocalizedsystemscoupledtoheatbathsand/orsubjecttonoise.Wealsomadeprogressonthisthemeinthepastyear,injointworkwithDr.JamirMarino,apostdocwhowaspaidpartiallythroughthisgrant,whohassincemovedontoafacultypositionattheUniversityofMainz.Thistooktheformofthreecompletedprojectsdescribedbelow.(xxii) RemnantsofAndersonlocalizationinpre-thermalizationinducedbywhitenoiseS.

Lorenzo,T.Apollaro,G.M.Palma,R.Nandkishore,A.SilvaandJ.Marino,Phys.Rev.B98,054302(2019)

Westudythenon-equilibriumevolutionofaone-dimensionalquantumIsingchainwithspatiallydisordered,time-dependent,transversefieldscharacterizedbywhitenoisecorrelationdynamics.Weestablishpre-thermalizationinthismodel,showingthatthequenchdynamicsoftheon-sitetransversemagnetizationfirstapproachesametastablestateunaffectedbynoisefluctuations,andthenrelaxesexponentiallyfasttowardsaninfinitetemperaturestateasaresultofthenoise.Wealsoconsiderenergytransportinthemodel,startingfromaninhomogeneousstatewithtwodomainwallswhichseparateregionscharacterizedbyspinswithoppositetransversemagnetization.WeobserveatintermediatetimescalesaphenomenologyakintoAndersonlocalization:


energyremainslocalizedwithinthetwodomainwalls,untiltheMarkoviannoisedestroyscoherenceandaccordinglydisorderinducedlocalization,allowingthesystemtorelaxtowardsthelatestagesofitsnon-equilibriumdynamics.WebenchmarkourresultswiththesimplercaseofanoisyquantumIsingchainwithoutdisorder,andwefindthatthepre-thermalplateauisagenericpropertyofweaklynoisyspinchains,whilethephenomenonofpre-thermalAndersonlocalisationisaspecificfeaturearisingfromthecompetitionofnoiseanddisorderinthereal-timetransportpropertiesofthesystem.


(xxiii) ManybodylocalizationproximityeffectsinplatformsofcoupledspinsandbosonsJ.MarinoandR.M.Nandkishore,Phys. Rev. B 97, 054201 (2018)

Inthisworkwediscusstheonsetofmanybodylocalizationinaone-dimensionalsystemcomposedofaXXZquantumspinchainandaBose-Hubbardmodellinearlycoupledtogether.Weconsidertwocomplementarysetupsdependingwhetherspatialdisorderisinitiallyimprintedonspinsoronbosons;inbothcases,weexploretheconditionsforthedisorderedportionofthesystemtolocalizebyproximityoftheothercleanhalf.Assumingthatthedynamicsofoneofthetwopartsdevelopsonshortertimescalesthantheother,wecanadiabaticallyeliminatethefastdegreesoffreedom,andderiveaneffectiveHamiltonianforthesystem'sremainderusingprojectionoperatortechniques.Performingalocatorexpansiononthestrengthofthemany-bodyinteractiontermoronthehoppingamplitudeoftheeffectiveHamiltonianthusderived,wepresentresultsonthestabilityofthemanybodylocalizedphasesinducedbyproximityeffect.Wealsobrieflycommentonthefeasibilityoftheproposedmodelthroughmodernquantumopticsarchitectures,withthelong-termperspectivetorealizeexperimentally,incompositeopensystems,Andersonormany-bodylocalizationproximityeffects.

This work is published.

(xxiv)Exploringmany-bodylocalisationinopenquantumsystemsviaWegner-Wilsonflows.ShaneP.Kelly,RahulNandkishoreandJamirMarino,Nucl.Phys.B951,114886(2020)WeapplyaFlowEquationmethodtostudytheproblemofamany-bodylocalisedsystemofspinlessfermions,coupledviadensity-densityinteractionstoasecondcleanchainoffermions.Inparticular,wefocusontheconditionsfortheonsetofamany-bodylocalisedphaseinthecleansectorofourmodelbyproximitytothedirtyone.Wefindthatamany-bodylocalisationproximityeffectinthecleancomponentisestablishedwhenthedensityofdirtyfermionsexceedsathresholdvalue,inawayreminiscentofrecentexperimentsonmanybodylocalisedsystemscoupledtoabath.Tuningthecontrolparametersofthemodelweestablishthresholdsfortheinductionofamany-bodylocalisedphaseinthecleansector,usingajointsetofemergentintegralsofmotionforthecleananddirtycomponentsasansatzforthesolutionoftheflowequations.Furthermore,byengineeringthegeometryoftheinter-chaincouplings,we


showthatthedynamicsofthemodelcanbedescribed,onintermediatetimescales,byaHamiltonianwithanovelsetofemergentintegralsofmotion.


(xxv) Disordercontrolledrelaxationina3DHubbardmodelquantumsimulator.W.Morong,

S.R.Muleady,I.Kimchi,W.Xu,R.M.Nandkishore,A.M.Rey,B.DeMarco.arXiv:2001.07341

Understandingthecollectivebehaviorofstronglycorrelatedelectronsinmaterialsremainsacentralprobleminmany-particlequantumphysics.AminimaldescriptionofthesesystemsisprovidedbythedisorderedFermi-Hubbardmodel(DFHM),whichincorporatestheinterplayofmotioninadisorderedlatticewithlocalinter-particleinteractions.Despiteitsminimalelements,manydynamicalpropertiesoftheDFHMarenotwellunderstood,owingtothecomplexityofsystemscombiningout-of-equilibriumbehavior,interactions,anddisorderinhigherspatialdimensions.Here,westudytherelaxationdynamicsofdoublyoccupiedlatticesitesinthethree-dimensional(3D)DFHMusinginteraction-quenchmeasurementsonaquantumsimulatorcomposedoffermionicatomsconfinedinanopticallattice.Inadditiontoobservingthewidelystudiedeffectofdisorderinhibitingrelaxation,wefindthatthecooperationbetweenstronginteractionsanddisorderalsoleadstotheemergenceofadynamicalregimecharacterizedbydisorder-enhancedrelaxation.Tosupporttheseresults,wedevelopanapproximatenumericalmethodandaphenomenologicalmodelthateachcapturetheessentialphysicsofthedecaydynamics.OurresultsprovideatheoreticalframeworkforapreviouslyinaccessibleregimeoftheDFHManddemonstratetheabilityofquantumsimulatorstoenableunderstandingofcomplexmany-bodysystemsthroughminimalmodels.

ThisworkisunderreviewandcurrentlyavailableonthearXiv.

Studenttheses

TwoPhDtheseswerecompletedpartiallywithsupportfromthisgrant.ThefirstwasbyDr.AbhinavPrem,nowapostdoctoralfellowatthePrincetonCenterforTheoreticalScience.ThetitleofthisthesisisAspects of Topology in Quantum Phases of Matter: A Journey through Lands both Flat and Not. The AFOSR supported work included therein is published, as publication 6 in the list at the beginning of this report. The full thesis can be obtained online from the University of Colorado library. The second PhD thesis was by Dr. Albert Schmitz, now a research scientist at Intel Corp. This thesis was entitled Linear Gauge Structures: Theory and Uses. The AFOSR supported portions of this thesis were published as publications 14 and 15, and also preprints 3 and 4 in the list at the beginning of this report. The full thesis can be obtained online from the University of Colorado library.


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Rahul Nandkishore REGENTS OF THE UNIVERSITY OF COLORADO …