Strongly Coupled Field Theories for Condensed Matter and Quantum Information Theory: Proceedings, International Institute of Physics, Natal, Rn, ... Proceedings in Physics (239), Band 239) PDF
Preview Strongly Coupled Field Theories for Condensed Matter and Quantum Information Theory: Proceedings, International Institute of Physics, Natal, Rn, ... Proceedings in Physics (239), Band 239)
Springer Proceedings in Physics 239 Alvaro Ferraz Kumar S. Gupta Gordon Walter Semenoff Pasquale Sodano Editors Strongly Coupled Field Theories for Condensed Matter and Quantum Information Theory Proceedings, International Institute of Physics, Natal, Rn, Brazil, 2–21 August 2015 Springer Proceedings in Physics Volume 239 Indexed by Scopus The series Springer Proceedings in Physics, founded in 1984, is devoted to timely reports of state-of-the-art developments in physics and related sciences. Typically based on material presented at conferences, workshops and similar scientific meetings, volumes published in this series will constitute a comprehensive up-to-date source of reference on a field or subfield of relevance in contemporary physics. Proposals must include the following: – name, place and date of the scientific meeting – a link to the committees (local organization, international advisors etc.) – scientific description of the meeting – list of invited/plenary speakers – an estimate of the planned proceedings book parameters (number of pages/ articles, requested number of bulk copies, submission deadline). More information about this series at http://www.springer.com/series/361 Alvaro Ferraz Kumar S. Gupta (cid:129) (cid:129) Gordon Walter Semenoff (cid:129) Pasquale Sodano Editors Strongly Coupled Field Theories for Condensed Matter and Quantum Information Theory Proceedings, International Institute of Physics, – Natal, Rn, Brazil, 2 21 August 2015 123 Editors Alvaro Ferraz Kumar S.Gupta International Institute of Physics-UFRN Theory Division Natal-Rn, RioGrande doNorte, Brazil SahaInstitute of NuclearPhysics Kolkata, India Gordon Walter Semenoff Department ofPhysics andAstronomy PasqualeSodano University of British Columbia International Institute of Physics-UFRN Vancouver, BC,Canada Natal-Rn, RioGrande doNorte, Brazil ISSN 0930-8989 ISSN 1867-4941 (electronic) SpringerProceedings in Physics ISBN978-3-030-35472-5 ISBN978-3-030-35473-2 (eBook) https://doi.org/10.1007/978-3-030-35473-2 ©SpringerNatureSwitzerlandAG2020 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. 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Preface The discovery and the control of new quantum behaviors of strongly interacting systemsisbynowacrucialissuefortheadvancementofthequantumtechnologies needed for quantum information processing and quantum devices. The aim of engineering and manipulating new classes of quantum devices poses, at the same time, many fundamental science problems since one has to describe the collective behavior of strongly interacting quantum particles when they are confined to per- tinent geometries and topologies at the nanometer scale. It is well known that, as one proceeds to smaller and smaller length scales, quantum properties can be substantially modified by the presence of interactions andcorrelationsleadingtotheemergenceofnon-perturbativeregimeswhichcannot be described by conventional mean-field theory approaches. In their most spec- tacularform,interactionsatthenanoscaleleadtostronglycorrelatedstatesofmatter already evidenced in fractional quantum Hall fluids, high critical temperature superconductors, some topological insulators and superconductors, graphene bilayers,andin“syntheticmaterials”suchasJosephsonsuperconductingnetworks and arrays, or junctions of quantum wires and one-dimensional ultracold atomic systems.Inmanyinstances,non-perturbative,aswellascounterintuitive,properties of these materials may be used to engineer new platforms for the solid-state implementation of quantum devices. Impurities are ubiquitous in condensed matter systems: the discovery of the Kondo effect and of Anderson localization have brought to the forefront their relevanceforstabilizingnewandunexpectedbehaviorsofaquantumsystem.When realized in a condensed matter system, such features are expected as emergent phenomena.Thereis,indeed,growingevidencethatbyjudiciouslyengineeringthe coupling of impurities to their environment, i.e., to the other modes of the con- densed matter system containing the impurity, one can: (A) Setnewstablephases,frustratedecoherence,andfacilitateenhancedresponses to external perturbations in quantum devices; (B) Engineer devices useful for topological quantum computation; vii viii Preface (C) Generatelong-distancecorrelations(entanglement)andimprovetheefficiency of quantum communication in spin systems; (D) Apply to the engineering of solid-state devices analytical methods recently developed in string and boundary conformal field theories. Paradigmatic examples of experimentally well controllable systems, where Kondo-like impurities lead to the emergence of new behaviors relevant for their applications to quantum devices, are provided by spin chains, ultracold atoms trappedinopticallattices,anti-dotsinfractionalquantumHall(FQH)systems,and junctions of either quantum wires or superconducting Josephson junction arrays. For these systems, boundary field theories together with the Tomonaga–Luttinger liquiddescriptionhavebeenprovidingusefulinsightsfortheexistenceofnewfixed pointsescapingconventionalmean-fieldtheoryanalysesaswellasforestablishing remarkable connections with Kondo physics. It is by now well known that progresses in condensed matter physics and other disciplinesmayinfluenceeachother.Longago,thestudyofsuperconductivityhas been closely related to structures underlying the standard model of elementary particlephysicssuchasspontaneoussymmetrybreakingandtheHiggsmechanism. Agenerationlater,theunderstandingofrenormalizationinfieldtheoriesdescribing elementaryparticleswasbeautifullymirroredinanalmostcompletesolutionofthe theory of critical phenomena and second-order phase transition. Inmorerecentyears,inadditiontoquantumfieldtheory,somenewapproaches have entered the fray. In fact, condensed matter theory has been more and more informed by string theory, through the holographic study of strongly coupled systems. This approach maps certain quantum dynamical systems in their strong coupling limit onto purely classical gravitational systems in higher dimensions; questions about the highly correlated deep quantum limit of the dynamical system arethenansweredbysolvingtheEinsteinequationswhichgovernclassicalgravity. This has the promise of a quantitative approach to certain quantum systems in the limit where the interactions among their constituents are very strong, to the point where their analysis is inaccessible to any other known analytic technique short of brute force numerical simulations.Not only wouldthis strongly correlated limit be analyzable in a quantitative way, but it would be systematically correctable. Whetheritcanbeusedtostudyrealisticmodelsofcondensedmattersystemsisstill an open question which is currently under investigation. At the very least, this approach will provide models which give a qualitative description of entirely new statesofmatterand,moreimportantly,newparadigmswhichshouldaidphysicists inunderstandingandclassifyingthebehaviorofsuchsystems.Thisideaisrelevant since some unsolved problems in condensed matter physics—such as high- temperature superconductivity or heavy fermion systems—almost invariably involve strong coupling physics and perhaps new states of matter. Condensed matter physics shows also an interesting interface with quantum informationtheory.Infact,condensedmatterphysicistsaregraduallylearningthat, in a study of the states of a quantum mechanical system with a large number of degrees of freedom, there is invariably an advantage to be gained in taking into Preface ix account the quantum information that is stored in the states, and in describing the states themselves in an information-theoretic framework. The storage, transport, and manipulation of quantum information have become relevant issues in modern condensed matter physics; for instance, systems with minimal environmental decoherence will no doubt lead to many interesting developments for condensed matter. Moreover, one of the most utile diagnostics of the storage of quantum information, the entanglement entropy, in strongly coupled systems is, these days, in many examples, computed using a string theory holographic formula. Anotherlineofdevelopmentisanewinterfacewithmathematicsandconsidersthe classificationofthetopologicalphases ofmattersuchastopologicalinsulatorsand topologicalsuperconductors.TheK-theoreticalclassificationoftopologicalinsulators istheprototypicalexample.Thissubjectisonlyatitsbeginning,asthemostcomplete developmentssofarapplyonlytonon-interactingandtoweaklyinteractingsystems. Afullunderstandingofthetopologicalphasesofstronglycorrelatedmatterisstillan openproblem.Approachestothisproblemcouldwellmakeuseofholographicduality and already have made use of ideas from quantum information theory. Properties ofthereduceddensitymatrixandtheinformationaboutquantumentanglementthat theycontain,forexample,arethoughttocarrytheinformationastowhetherasystem is in a “topological” or a “non-topological” phase. It is likely that string theory holographywillhavesomethingtosayaboutthesesystemsatstrongcoupling. Anotherimportantinterfaceofcondensedmatteriswithatomicphysicsandcold atoms. Cold atoms provide an experimental technique where important statistical mechanicalsystemscanbeengineeredandstudiedinawidearrayofcircumstances. Analogsofsystemswhicharestronglycorrelatedintherealworldcanbesimulatedat variousvaluesofthecouplingandstudiesinavarietyofregimes.Thisiscombined withthefactthattheexperimentalmeasurementsthatcanbeperformedonacoldatom systemareoftencomplementarytothoseavailableinthecondensedmattersystem. Thishasthepotentialofyieldingunprecedentedinformationaboutmodels,likethe Hubbardmodel,inregimes whichareimportantfor theirphysical applications,for example,intheregimewheretheymodelhigh-temperaturesuperconductivity. Recently,newlow-energyneutralfermionicexcitations(Majoranaedgemodes) have been claimed to be relevant in a variety of condensed matter systems, also providingnewinsightsfortheinvestigationofnon-Fermiliquidstatesincorrelated systems.Majoranafermionswerefirstproposedin1937byEttoreMajorana(19)who consideredamodificationtotherelativisticDiracequationforconventionalspin½ particles (Dirac fermions) that gave purely real (as opposed to complex) solutions. TheseMajoranafermionsareparticlesthataretheirownantiparticles—theircreation operatorinquantumtheoryisequaltotheirannihilationoperator,unlikethecasefor conventional(Dirac)fermionssuchaselectronsandholeswhicharedifferentdueto theiroppositecharge.Beingrealtheyareneutralexcitations. Low-energy Majorana modes have been recently the object of many theoretical and experimental investigations. Located at the edges of one-dimensional (1D) devices are responsible for the emergence of stretched non-local electron states allowing for distance-independent tunneling, crossed Andreev reflection, x Preface teleportation-like coherent transfer of a fermion, and fractional Josephson effects. Their effects emerge in a variety of condensed matter platforms. ThehugeinterestinMajoranafermionsgoesbeyondfundamentalcuriositysince there is enormous potential for future quantum information technology if devices can be made based on manipulation of Majorana fermions, which are effectively fractionalized particles (anyons) obeying non-Abelian rather than Fermi–Dirac statistics. This would allow a qubit to be stored non-locally in a pair of widely separated Majorana bound states. These could be more insensitive to the effect of local sources of decoherence, which is currently the major obstacle to realizing a scalable quantum computer. Onecaneasilyconvinceoneselfthatthebreadthofthetechnicalskillsneededto synthesize these research directions is truly staggering. Condensed matter systems such as high Tc superconductors, topological insulators, and superconductors, and Kondo systems realized with pertinently engineered quantum devices all exhibit a variety of new behaviors, which may be accounted by pertinent strongly coupled fieldtheories.Thebookwillprovideaninsightfulpanoramaonsomeofthesetopics emphasizing interesting connections between them. The contents are based on the lectures given attheprogram (conference +workshop)on“Strongly CoupledField Theories for Condensed Matter and Quantum Information Theory” held at the InternationalInstituteofPhysicsinNatalduringAugust2015.Thebooksufferedan undue delay caused by a serious illness of the corresponding editor who is very grateful to all the authors for the extra effort done in updating their lectures. Acknowledgements: We thank all the IIP staff for the qualified help given duringtheConferenceandWorkshopheldinNatal.WethankMargarethBarqueiro andBiaPessoa for theirkind andefficienthelp inassistingusduringallthestages of the conference and for taking good care of all the organizational tasks. In addition,weareverygratefultoMargarethBarqueiroforhelpinginthepreparation of this book; without her qualified help, we could not have prepared the final versionsubmittedtotheeditor.P.S.isverygratefultoIIP,Natal,forastimulating and pleasant hospitality at the Institute from Aug 2011 to October 2016; unfortu- nately, his stay suddenly terminated due to a very serious illness (He partially recovered at last!). Two of us (P. S. and A. F.) are grateful to the Ministry of Science, Technology, Innovation and Communication (MCTIC) and to the CNPq for financial support for granting them a “Bolsa de Produtividade em Pesquisa”. Finally, we also want to acknowledge the agencies CAPES and CNPq for the support given for our Workshop/Conference as well as the Minister of Education for generously supporting the IIP throughout the past years. Natal-Rn, Brazil Alvaro Ferraz Kolkata, India Kumar S. Gupta Vancouver, Canada Gordon Walter Semenoff Natal-Rn, Brazil Pasquale Sodano
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