Chiral Gravitons in Topological Quantum Matter: From Solid-State Materials to Quantum Computers

A major open problem in modern physics is the table-top generation and detection of emergent particles analogous to gravitons: the elusive mediators of gravitational force in a quantum theory of gravity. In solid state materials, recent work by Haldane has pointed out that fractional quantum Hall (FQH) phases of matter host graviton-like excitations as they respond to the curvature of space they live in. Unfortunately, direct experimental observation of gravitons in FQH phases remains a challenge. This project will explore the possibility of recreating a similar kind of physics in the emerging quantum technology machines, e.g., ultracold atoms in optical lattices and quantum computers made of trapped ions. You will investigate how graviton-like particles and their dynamics could be controllably created and measured in such systems. To accomplish this task, your project will advance the understanding of geometrical degrees of freedom of fractional quantum Hall states, and then apply this knowledge to design quantum algorithms that can efficiently simulate graviton dynamics using the existing quantum hardware.

<p>Fractional quantum Hall effect (FQHE) is a phenomenon where&nbsp;electrons form exotic types of quantum liquids by fractionalising into&nbsp;new kind of particles called&nbsp;anyons. Recent experiments have observed signatures of these exotic particles:&nbsp;<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>&nbsp;However, the physics&nbsp;of FQHE is not fully described by anyone&nbsp;&ndash;&nbsp;these phases of matter 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 shown that the exotic graviton dynamics in FQHE phases can be captured in a simple qubit model that can be directly&nbsp;simulated on the&nbsp;IBM quantum computer.&nbsp;</p> <p>One of the goals of this&nbsp;project will be to understand the dynamics in the more complex non-Abelian FQHE phases, whose underlying anyon particles have exchange statistics which is fundamentally different from fermions and bosons. The second goal of the project is&nbsp;to investigate the dynamics of so-called&nbsp;higher-spin excitations in FQHE phases, which can be viewed as cousins of the &ldquo;graviton&rdquo; particle (which carries spin-2). The insights from such a&nbsp;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:&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] &ldquo;Geometric Description of the Fractional Quantum Hall Effect&rdquo;, F. D. M. Haldane, Phys. Rev. Lett.&nbsp;107, 116801 (2011).<br /> [2] &ldquo;Realizing Fractional-Quantum-Hall Gravitons on Quantum Computers&rdquo;,&nbsp;Ammar Kirmani,&nbsp;Kieran Bull,&nbsp;Chang-Yu Hou,&nbsp;Zlatko Papic,&nbsp;Armin Rahmani,&nbsp;Pouyan Ghaemi,&nbsp;https://arxiv.org/abs/2107.10267.</p>

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University&#39;s website</a>. Please state clearly the Planned Course of Study that you are applying for <em><strong>PHD Physics &amp; Astronomy FT</strong></em> and in the research information section&nbsp;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>&nbsp;as well as&nbsp;<a href="https://eps.leeds.ac.uk/physics/staff/4124/dr-zlatko-papic">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 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. &nbsp;Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application. &nbsp;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>Please note that you must provide the following documents in support of your application by the closing date of 28 June 2024:</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> <li>Funding information:&nbsp; Leverhulme Trust</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>A highly competitive Leverhulme Trust, 3.5 Year PhD Studentship&nbsp;paying academic fees at the Home Fee Rate of &pound;4,712 for Session 2023/24, together with a maintenance grant of &pound;18,622 for 3.5 years.</p> <p>This opportunity is open to UK applicants only. All candidates will be placed into the Leverhulme Trust Studentship Competition and selection is based on academic merit.</p> <p>Please refer to the&nbsp;<a href="https://www.ukcisa.org.uk/">UKCISA</a>&nbsp;website for information regarding Fee Status for Non-UK Nationals.</p>

<p>For further information about your application, please contact Doctoral College Admissions,<br /> e: <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,<br /> e:&nbsp;<a href="mailto:Z.Papic@leeds.ac.uk">Z.Papic@leeds.ac.uk</a></p>