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Dynamics in Topological Phases of Matter


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Key facts

Type of research degree
Application deadline
Ongoing deadline
Project start date
Friday 1 October 2021
Country eligibility
International (open to all nationalities, including the UK)
Competition funded
Source of funding
University of Leeds
Dr Zlatko Papic
School of Physics and Astronomy
Research groups/institutes
Theoretical Physics
<h2 class="heading hide-accessible">Summary</h2>

Phases of matter like magnets or water can be understood by studying the individual atoms that form them. In the last three decades, other types of materials have been discovered which cannot be understood in this simple approach. In such materials, quantum mechanics and strong correlations force the particles to lose their identity and form collective quantum states that resemble complicated loops and braids. These &amp;ldquo;topological phases of matter&amp;rdquo; have profoundly enriched our understanding of quantum matter (which was also recognised by the 2016 Nobel physics prize), and they are currently being utilised for practical applications in terms of new ways of storing and manipulating quantum information, which is protected from from many sources of errors. This PhD project will investigate novel types of dynamics in topological phases of matter, in particular focusing on their geometric degrees of freedom that can be described by gravitational Chern-Simons field theory.

<h2 class="heading hide-accessible">Full description</h2>

<p>One of the best studied examples of topological phases is the so-called&nbsp;fractional quantum Hall effect&nbsp;(FQHE). Under experimental conditions of the FQHE, electrons form exotic types of quantum liquids where they fractionalise into new kind of particles called&nbsp;anyons. The reason why this happens has to do with topology, which is experimentally imposed by an applied magnetic field. In recent years, from the work of Haldane [1] and others, it has been realised that topology does not fully describe FQHE phases &ndash; these phases also have emergent degrees of freedom which have&nbsp;geometric&nbsp;character. This means that their quantised excitations behave like an analog of the elusive graviton particle in theories&nbsp;of quantum gravity.</p> <p>This PhD project will investigate dynamics of fractional quantum Hall phases, in particular focusing on their geometric degrees of freedom. While the equilibrium properties of the FQHE have been well understood due to major theoretical efforts of the past three decades, the study of non-equilibrium dynamics of FQHE phases is an uncharted territory. In our recent work [2], we have addressed this question for the first time and we have shown that FQHE phases have rich dynamical properties, in particular they allow us to probe the mentioned &ldquo;graviton&rdquo; excitation and observe its dynamics after the FQHE system is &ldquo;quenched&rdquo; (i.e., the direction of the external magnetic field is suddenly changed).</p> <p>One of the goals of the project will be to understand the dynamics in the so-called non-Abelian FQHE phases, whose underlying particles have exchange statistics which is fundamentally different from fermions and bosons. It is precisely this type of statistics that allows to use such systems to perform &ldquo;topological quantum computation&rdquo;.&nbsp;The second goal of the project would be to investigate the dynamics of higher-spin excitations in FQHE phases, which can be viewed as generalisations of the &ldquo;graviton&rdquo; particle (which carries spin-2). The study of such exotic excitations would not only shed light on the richness of structure in FQHE phases, but the insights gained from it might prove to be of interest in various other areas of theoretical physics which have focused on higher-spin symmetry (e.g., generalization of gauge/gravity dualities, large N gauge theory, etc.).</p> <p>Desired student background:&nbsp;We seek talented and highly-motivated physics students to pursue this project in the general area of quantum condensed matter physics and topological phases. The project will involve numerical modelling of fractional quantum Hall systems via&nbsp;exact diagonalisation and related techniques (e.g., matrix product states, DMRG, etc.).&nbsp;The project is thus particularly suitable for those with strong interest in computational physics and numerical simulations.</p> <h5>References</h5> <p>[1]&nbsp;Geometric Description of the Fractional Quantum Hall Effect, F. D. M. Haldane, Phys. Rev. Lett.&nbsp;107, 116801 (2011).<br /> [2]&nbsp;Geometric quench and non-equilibrium dynamics of fractional quantum Hall states, Zhao Liu, Andrey Gromov and Zlatko Papic, arXiv:1803.00030.</p>

<h2 class="heading">How to apply</h2>

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="">University&#39;s website</a>. Please state clearly in the research information section&nbsp;that the research degree you wish to be considered for is &ldquo;Dynamics in Topological Phases of&nbsp;Matter&rdquo; as well as&nbsp;<a href="">Dr Zlatko Papic</a>&nbsp;as your proposed supervisor.</p> <p>If English is not your first language, you must provide evidence that you meet the University&#39;s minimum English language requirements (below).</p> <p><em>We welcome applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates. All scholarships will be awarded on the basis of merit.</em></p>

<h2 class="heading heading--sm">Entry requirements</h2>

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

<h2 class="heading heading--sm">English language requirements</h2>

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid.

<h2 class="heading">Funding on offer</h2>

<p>A highly competitive Leverhulme Trust, 4 Year PhD Studentship&nbsp;paying academic fees at the Home Fee Rate of &pound;4,600 in Session 2021/22, together with a maintenance grant of &pound;16,170 for 4&nbsp;years.</p> <p>This opportunity is open to all applicants. All candidates will be placed into the Leverhulme Trust Studentship and selection is based on academic merit.</p> <p>The&nbsp;<a href="">UKCISA</a>&nbsp;website will be updated in due course with information regarding Fee Status for Non-UK Nationals starting from September/October 2021.</p>

<h2 class="heading">Contact details</h2>

<p>For further information regarding the application procedure, please contact Doctoral College Admissions,<br /> e: <a href=""></a>, t: +44 (0)113 343 5057.</p> <p>For further information regarding the application procedure, please contact Dr Zlatko Papic,<br /> e:&nbsp;<a href=""></a></p>

<h3 class="heading heading--sm">Linked research areas</h3>