Springer Theses Recognizing Outstanding Ph.D. Research Adam Smith Disorder-Free Localization Springer Theses Recognizing Outstanding Ph.D. Research Aims and Scope The series “Springer Theses” brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected foritsscientificexcellenceandthehighimpactofitscontentsforthepertinentfield of research. For greater accessibility to non-specialists, the published versions includeanextendedintroduction,aswellasaforewordbythestudent’ssupervisor explainingthespecialrelevanceoftheworkforthefield.Asawhole,theserieswill provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. Finally, it provides an accredited documentation of the valuable contributions made by today’s younger generation of scientists. 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More information about this series at http://www.springer.com/series/8790 Adam Smith Disorder-Free Localization Doctoral Thesis accepted by the University of Cambridge, Cambridge, UK 123 Author Supervisor Dr. AdamSmith Dmitry Kovrizhin Fakultät für Physik ClarendonLaboratory,RudolfPeierlsCentre Technische UniversitätMünchen ForTheoretical Physics Garching,Germany University of Oxford Oxford,UK ISSN 2190-5053 ISSN 2190-5061 (electronic) SpringerTheses ISBN978-3-030-20850-9 ISBN978-3-030-20851-6 (eBook) https://doi.org/10.1007/978-3-030-20851-6 ©SpringerNatureSwitzerlandAG2019 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained hereinorforanyerrorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregard tojurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland To my parents. ’ Supervisor s Foreword It is my pleasure to write this foreword for Adam Smith’s thesis. Sinceitsdiscovery,thephenomenonofAndersonlocalizationhasbeenfoundto playanever-increasingroleinourunderstandingofcondensedmatterphysics,from the quantum Hall effect to more recent studies of many-body localization. This thesis presents another unexpected manifestation of Anderson localization phenomenology in the setting of Z lattice gauge theories. Theoretical studies of 2 lattice gauge theories have been an important topic in theoretical physics, in both high-energyandcondensedmattercommunities.Inthelatter,theyariseaseffective descriptionsof strongly correlated systems,andthe models discussed inthis thesis are closely related to the famous Hubbard model and Kitaev’s toric code. This work may shed a new light on the physics of these models by looking at their behaviour in a non-equilibrium setting, where there is apparently a very rich phenomenology, which bridges between recent important ideas in quantum dis- entangled liquids and many-body localization. Oneoftheappealsofthisworkformeisthatitshowsconclusivelyforthefirst time that localization is possible in the absence of disorder. Such a possibility was first considered in early works onHe-3and He-4 mixtures in the80sby myPh.D. advisors Yuri Kagan and Leonid Maksimov. Since then, many people have been trying to devise models where disorder-free localization manifests itself. Adam’s work presents such a setting for the first time. From the technical perspective, this work is also quite beautiful. To my knowledge, this is the first time one can perform calculations essentially in a thermodynamic limit because of self-averaging property due to emergent disorder. This remarkable feature of the model also allows one to study out-of-time-ordered correlators, which have recently attracted a great deal of attention. For a micro- scopicquantummany-bodysystem,thistaskhaspreviouslybeenachievedonlyin a very small number of systems, including the quantum Ising model and rather special quantum circuit models. Using thisopportunity,Iwouldliketothankourcollaborators JohannesKnolle andRoderichMoessner.It hasbeenapleasuretoworkwith both ofthem overthe years,andAdamisluckytohavebeenworkingcloselywiththemduringhisPh.D. vii viii Supervisor’sForeword Non-equilibrium problems in strongly correlated systems, and more recently includinglatticegaugetheories,havebeenplayinganincreasinglyimportantrolein thestudiesofinteractingmany-bodysystems.Lookingahead, Ihopetheresultsof this thesis will find useful applications in these activities. Oxford, UK Dmitry Kovrizhin April 2019 Abstract The venerable phenomena of Anderson localization, along with the more recent many-bodylocalization(MBL),dependcruciallyonthepresenceofdisorder.Here weintroduceafamilyofsimpletranslationallyinvariantmodelsoffermionslocally coupled to spins, which have a disorder-free mechanism for localization. This mechanismisduetoalocalZ gaugesymmetry,andweuncovertheconnectionto 2 lattice gauge theories. We diagnose the localization through long-time memory of initial conditions after a global quantum quench. One of the defining features of the models that we study is the binary nature of the emergent disorder, related to the Z degrees of freedom. This results in a 2 qualitatively different behaviour in the strong effective disorder limit compared to typicallystudiedmodelsoflocalization.Forexample,itgivesrisetothepossibility ofadelocalizationtransitionviaquantumpercolationinhigherthanonedimension. In connection to the recently proposed quantum disentangled liquid (QDL), we also study the entanglement properties of our models. The QDL provides an alternative to both complete localization and to the eigenstate thermalization hypothesis.OurmodelshighlightthesubtletyofdefiningaQDL,andweoffernew insights into their entanglement properties. While the simplest models we consider can be mapped onto free fermions, we also include interactions which lead to MBL-like behaviour characterized by log- arithmic entanglement growth. We further consider interactions that generate dynamics for the conserved charges, which give rise to only transient localization behaviour, or quasi-MBL. Finally, we present a proposal for the experimental measurement of gauge field correlators for our model in two dimensions. This proposal is based on interfero- metric techniques which are feasible using current experimental capabilities. Furthermore, the interacting generalizations of our models can be similarly implemented in experiments, providing access to the dynamics of strongly inter- actinglatticegaugetheories,beyondwhatcanbesimulatedonaclassicalcomputer. ix Publications Related to this Thesis The core part of the thesis is based on research appearing in: [1] A. Smith, J. Knolle, R. Moessner, and D. L. Kovrizhin, “Logarithmic spreading of out-of-time-ordered correlators without many-body localiza- tion”, arXiv:1812.07981 (preprint) [2] A. Smith, J. Knolle, R. Moessner, and D. L. Kovrizhin, “Dynamical local- ization in Z lattice gauge theories”, Phys. Rev. B 97, 245137 (2018) 2 [3] A.Smith,D.L.Kovrizhin,R.Moessner,andJ.Knolle,“Dynamicsofalattice gauge theory with fermionic matter – minimal quantum simulator with time-dependent impurities in ultracold gases”, Quantum Sci. Technol. 3, 044003 (2018) [4] A. Smith, J. Knolle, R. Moessner, and D. L. Kovrizhin, “Absence of Ergodicity without Quenched Disorder: from Quantum Disentangled Liquids to Many-Body Localization”, Phys. Rev. Lett. 119, 176601 (2017) [5] A. Smith, J. Knolle, D. L. Kovrizhin, and R. Moessner, “Disorder-free localization”, Phys. Rev. Lett. 118, 266601 (2017) Other works published during my doctoral research not included in this thesis: [6] A. Smith, J. Knolle, D. L. Kovrizhin, J. T. Chalker, and R. Moessner, “Majoranaspectroscopyofthree-dimensionalKitaevspinliquids”,Phys.Rev. B 93, 235146 (2016) [7] A. Smith, J. Knolle, D. L. Kovrizhin, J. T. Chalker, and R. Moessner, “Neutron scattering signatures of the 3D hyperhoneycomb Kitaev quantum spin liquid”, Phys. Rev. B 92, 180408(R) (2015) xi