Upload
others
View
1
Download
0
Embed Size (px)
Citation preview
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
DISTRIBUTION A: Distribution approved for public release.
AF Office Of Scientific Research (AFOSR)/ RTB1Arlington, Virginia 22203
Air Force Research Laboratory
Air Force Materiel Command
DISTRIBUTION A: Distribution approved for public release
a. REPORT
Unclassified
b. ABSTRACT
Unclassified
c. THIS PAGE
Unclassified
REPORT DOCUMENTATION PAGE Form ApprovedOMB No. 0704-0188
The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Executive Services, Directorate (0704-0188). Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ORGANIZATION.1. REPORT DATE (DD-MM-YYYY)
17-09-20202. REPORT TYPE
Final Performance3. DATES COVERED (From - To)
01 Jul 2019 to 30 Jun 20204. TITLE AND SUBTITLENon-equilibrium dynamics and many body localization in ultracold atoms
5a. CONTRACT NUMBER
5b. GRANT NUMBERFA9550-17-1-0183
5c. PROGRAM ELEMENT NUMBER61102F
6. AUTHOR(S)Rahul Nandkishore
5d. PROJECT NUMBER
5e. TASK NUMBER
5f. WORK UNIT NUMBER
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)REGENTS OF THE UNIVERSITY OF COLORADO3100 MARINE ST 572 UCBBOULDER, CO 80309-0001 US
8. PERFORMING ORGANIZATIONREPORT NUMBER
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)AF Office of Scientific Research875 N. Randolph St. Room 3112Arlington, VA 22203
10. SPONSOR/MONITOR'S ACRONYM(S)AFRL/AFOSR RTB1
11. SPONSOR/MONITOR'S REPORTNUMBER(S)
AFRL-AFOSR-VA-TR-2020-0180 12. DISTRIBUTION/AVAILABILITY STATEMENTA DISTRIBUTION UNLIMITED: PB Public Release
13. SUPPLEMENTARY NOTES
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
16. SECURITY CLASSIFICATION OF: 17. LIMITATION OFABSTRACT
UU
18. NUMBEROFPAGES
19a. NAME OF RESPONSIBLE PERSONMETCALFE, GRACE
19b. TELEPHONE NUMBER (Include area code)703-696-9740
Standard Form 298 (Rev. 8/98)Prescribed by ANSI Std. Z39.18
Page 1 of 1FORM SF 298
9/29/2020https://livelink.ebs.afrl.af.mil/livelink/llisapi.dll
DISTRIBUTION A: Distribution approved for public release
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]
DISTRIBUTION A: Distribution approved for public release
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
DISTRIBUTION A: Distribution approved for public release
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.
DISTRIBUTION A: Distribution approved for public release
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.
Thisworkispublished.
(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
DISTRIBUTION A: Distribution approved for public release
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.
Thisworkispublished.
(vii) LocalizationfromHilbertspaceshattering:Fromtheorytophysicalrealizations.VedikaKhemani,MichaelHermeleandRahulNandkishore,Phys.Rev.B101,174204(2020)[Editors’suggestion]ThisworkcontinuesthestudyofthefractonicrandomcircuitmodelintroducedbythePIin(vi)above,andprovidesacompleteandrigorousanalyticunderstandingofthenewtypeoflocalizationarisingtherein.Specifically,thelocalizationinthismodelisrigorouslyshownasarisingfromaconstraintinduced`shattering’ofHilbertspaceintoahugenumberofdynamicallydistinctsubsectors.This`shattering’phenomenonisshown
DISTRIBUTION A: Distribution approved for public release
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
DISTRIBUTION A: Distribution approved for public release
aremeasurezerointhethermodynamiclimit.Inthiscase,genericinitialconditionsdothermalize,butwearguethattheydosoinsubdiffusivemanner.Weintroducenewclassesofhydrodynamictheoriestodescribethethermalizationofsuchfractonmatter.Eachofthesetheoriesexhibitssubdiffusivethermalization,andconstitutesanewuniversalityclassofhydrodynamicbehavior.Thereareinfinitelymanysuchclasses,eachwithdistinctsubdiffusiveexponents,allofwhicharecapturedbyourformalism.Ourframeworknaturallyexplainsrecentresultsondynamicswithconstrainedquantumcircuits,aswellasrecentexperimentswithultracoldatomsintiltedopticallattices.Weidentifycrispexperimentalsignaturesofthesenovelhydrodynamics,andexplainhowtheymayberealizedinneartermultracoldatomexperiments.
Thisworkispublished.
(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.
Thisworkispublished.
(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).
DISTRIBUTION A: Distribution approved for public release
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)
DISTRIBUTION A: Distribution approved for public release
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.
DISTRIBUTION A: Distribution approved for public release
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:
DISTRIBUTION A: Distribution approved for public release
energyremainslocalizedwithinthetwodomainwalls,untiltheMarkoviannoisedestroyscoherenceandaccordinglydisorderinducedlocalization,allowingthesystemtorelaxtowardsthelatestagesofitsnon-equilibriumdynamics.WebenchmarkourresultswiththesimplercaseofanoisyquantumIsingchainwithoutdisorder,andwefindthatthepre-thermalplateauisagenericpropertyofweaklynoisyspinchains,whilethephenomenonofpre-thermalAndersonlocalisationisaspecificfeaturearisingfromthecompetitionofnoiseanddisorderinthereal-timetransportpropertiesofthesystem.
Thisworkispublished.
(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
DISTRIBUTION A: Distribution approved for public release
showthatthedynamicsofthemodelcanbedescribed,onintermediatetimescales,byaHamiltonianwithanovelsetofemergentintegralsofmotion.
Thisworkispublished.
(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.
DISTRIBUTION A: Distribution approved for public release