Dynamics of Geometry in Topological Quantum Matter

Supervisor(s)

Contact Dr Zlatko Papic to discuss this project further informally.

Project description

Materials 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 “topological phases of matter” have profoundly enriched our understanding of quantum matter (which was also recognised by the 2016 Nobel physics prize [1]), 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 [2]. One of the best studied examples of topological phases is the so-called fractional quantum Hall effect (FQHE).

Under experimental conditions of the FQHE, electrons form exotic types of quantum liquids where they fractionalise into new kind of particles called 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 [3] and others, it has been realised that topology does not fully describe FQHE phases – these phases also have emergent degrees of freedom which have geometric character. This means that their quantised excitations behave like an analog of the elusive graviton particle in theory of quantum gravity. 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 [3], 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 “graviton” excitation and observe its dynamics after the FQHE system is “quenched” (i.e., the direction of the external magnetic field is suddenly changed).

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 “topological quantum computation” [2].) 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 “graviton” 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.).

References
[1] The Nobel Prize in Physics 2016 - Scientific background: Topological phase transitions and topological phases of matter, http://www.nobelprize.org/nobel_prizes/physics/laureates/2016/advanced.html
[2] A Short Introduction to Topological Quantum Computation, Ville Lahtinen and J. K. Pachos, arXiv:1705.04103 (2017).
[3] Geometric Description of the Fractional Quantum Hall Effect, F. D. M. Haldane, Phys. Rev. Lett. 107, 116801 (2011).
[4] Geometric quench and non-equilibrium dynamics of fractional quantum Hall states, Zhao Liu, Andrey Gromov and Zlatko Papic, arXiv:1803.00030.

Entry requirements

Applications are invited from candidates with or expecting a minimum of a UK upper second class honours degree (2:1), and/or a Master's degree in physics, or a relevant degree (e.g., mathematics). The candidate should be highly motivated, with strong analytical and problem solving skills. Background in theoretical physics, condensed matter physics, and numerical simulations would be beneficial.

If English is not your first language, you must provide evidence that you meet the University's minimum English Language requirements.

How to apply

Formal applications for research degree study should be made online through the university's website. Please state clearly in the research information section that the PhD you wish to be considered for is 'Dynamics of Geometry in Topological Quantum Matter' as well as Dr Zlatko Papic as your proposed supervisor.

We welcome scholarship 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.

If you require any further information please contact the Graduate School Office, e: maps.pgr.admissions@leeds.ac.uk