Dynamics of Topological Quantum Matter: From Solid-State Materials to Quantum Computers

Topological quantum matter can host emergent particles analogous to gravitons: the elusive mediators of gravitational force in a quantum theory of gravity. For example, in solid state materials, fractional quantum Hall (FQH) phases of electrons can host graviton-like excitations which respond to the effective curvature of their host material. This project will explore the possibility of recreating a similar kind of physics in the emerging quantum technology devices, e.g., ultracold atoms in optical lattices and quantum computers. You will investigate how graviton-like particles and their dynamics could be controllably created and measured in such systems. More broadly, this project will advance the understanding of geometrical degrees of freedom in topological quantum matter, which govern their dynamics and out-of-equilibrium responses.

<p>Fractional quantum Hall effect (FQHE) is a phenomenon where electrons form exotic types of quantum liquids by fractionalising into new kind of particles called anyons. Recent experiments have observed signatures of these exotic particles: <a href="https://www.quantamagazine.org/milestone-evidence-for-anyons-a-third-kingdom-of-particles-20200512/">https://www.quantamagazine.org/milestone-evidence-for-anyons-a-third-kingdom-of-particles-20200512/</a> However, the physics of FQHE is not fully described by anyons –these phases of matter also have additional degrees of freedom which have a geometric character. This means that their quantised excitations behave like an analog of the elusive graviton particle in theories 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 non-equilibrium dynamics of FQHE phases remains an uncharted territory. In our recent work [Phys. Rev. Lett. <strong>129</strong>, 056801 (2022)], we have shown that the exotic graviton dynamics in FQHE phases can be captured in a simple qubit model and directly simulated on the IBM quantum computer. </p> <p>One of the goals of this project will be to understand the dynamics in the more complex non-Abelian FQHE phases, whose underlying anyon particles are fundamentally different from fermions and bosons. The second goal of the project is to investigate the dynamics of so-called higher-spin excitations in FQHE phases, which can be viewed as cousins of the “graviton” particle (which carries spin-2). The insights from such a study may prove to be of interest in various other areas of theoretical physics which have focused on higher-spin symmetry (e.g., generalisation of gauge/gravity dualities, large N gauge theory, etc.).</p> <p>Desired student background: 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 exact diagonalisation and tensor network techniques. The project is thus particularly suitable for those with strong interest in computational physics and numerical simulations.</p>

<p>Formal applications for research degree study should be made online through the <a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University's website</a>. Please state clearly the Planned Course of Study that you are applying for <em><strong>PHD Physics & Astronomy FT,</strong></em> in the research information section that the research degree you wish to be considered for is <em><strong>Chiral Gravitons in Topological Quantum Matter: From Solid-State Materials to Quantum Computers</strong></em> as well as <a href="https://eps.leeds.ac.uk/physics/staff/4124/dr-zlatko-papic">Dr Zlatko Papic</a> as your proposed supervisor and in the finance section, please state clearly <em><strong>the funding that you are applying for, if you are self-funding or externally sponsored</strong></em>.</p> <p>If English is not your first language, you must provide evidence that you meet the University's minimum English language requirements (below).</p> <p style="text-align:start; margin-bottom:24px"><em>As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.</em></p> <p>Applications will be considered on an ongoing basis.  Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application. We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed.</p> <p style="margin-bottom:11px"><strong>Please note that you must provide the following documents in support of your application by the closing date of Friday 13 December 2024 if applying for the Bell Burnell Scholarship, Monday 6 January 2025 if applying for the China Scholarship Council-University of Leeds Scholarship, Monday 3 February 2025 if applying for Leeds Doctoral Scholarship or Tuesday 1 April 2025 for Leeds Opportunity Research Scholarship.</strong></p> <p>If you are applying with external sponsorship or you are funding your own study, please ensure you provide your supporting documents at the point you submit your application:</p> <ul> <li>Full Transcripts of all degree study or if in final year of study, full transcripts to date</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul>

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.

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.

<p style="margin-bottom:12px"><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p><strong>UK</strong> – The <a href="https://phd.leeds.ac.uk/funding/102-bell-burnell-scholarship-award-awarded-by-the-iop">Bell Burnell Scholarship Award</a> is available to support applicants who are from groups that are currently under-represented in physics (awarded by the IOP) <strong>(closing date: Friday 13 December 2024).</strong> The <a href="http://phd.leeds.ac.uk/funding/138-leeds-doctoral-scholarship-2025-faculty-of-engineering-and-physical-sciences#:~:text=Key%20facts&text=One%20Leeds%20Doctoral%20Scholarship%20is,rata%20for%20part%2Dtime%20study.">Leeds Doctoral Scholarship</a> <strong>(closing date: Monday 3 February 2025)</strong> and <a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a><strong> (closing date: Tuesday 1 April 2025)</strong> are available to UK applicants. <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p><strong>Non-UK</strong> – The <a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a> is available to nationals of China <strong>(closing date: Monday 6 January 2025)</strong>. The <a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a> is available to support US citizens. <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p>You will be responsible for paying the overtime fee in full in your writing up/overtime year (£320 in Session 2024/25), but the scholarship maintenance allowance will continue to be paid for up to 6 months in the final year of award.</p> <p><strong>Important:</strong> Please note that that the award does <em><strong>not</strong></em> cover the costs associated with moving to the UK.  All such costs (<a href="https://www.leeds.ac.uk/international-visas-immigration/doc/applying-student-visa">visa, Immigration Health Surcharge</a>, flights etc) would have to be met by yourself, or you will need to find an alternative funding source. </p> <p>Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.</p>

<p>For further information about your application, please contact PGR Admissions by email to <a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a></p> <p>For further information about this project, please contact Dr Zlatko Papic by email to <a href="mailto:Z.Papic@leeds.ac.uk">Z.Papic@leeds.ac.uk</a></p>