Disorder-Free Localization

152 Pages·2019·4.694 MB·English

by  Adam Smith

Springer Theses
Recognizing Outstanding Ph.D. Research
Adam Smith
Disorder-Free
Localization
Springer Theses
Recognizing Outstanding Ph.D. Research
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Adam Smith
Disorder-Free Localization
Doctoral Thesis accepted by
the University of Cambridge, Cambridge, UK
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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
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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.
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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.
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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)
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