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EPSRC DTP studentship: Dimer models on quasicrystals

Cardiff School of Physics and Astronomy

Cardiff United Kingdom Other Solid State Physics Theoretical Physics

About the Project

How many ways are there of tiling a chess board with dominoes? This is an example of a classical ’dimer model’. Removing one domino reveals the two squares it covered: one black, one white. These can be thought of as a particle-antiparticle pair, with further domino re-arrangements allowing the particles to move around on the board. This simple model turns out to have deep implications for strongly-interacting physical systems.

Condensed matter physics is the study of phenomena which emerge when huge numbers of particles interact. Recently, emergent particles have begun to be understood which appear as fractions of fundamental particles. For example, ’magnetic monopoles’, which behave like the isolated north or south poles of magnets able to move independently. The general phenomenon is termed ’fractionalization’. It forms the basis of our theories in some of the hottest topics in current research, from high-temperature superconductivity to fault-tolerant ’topological’ quantum computation.

This project will consider dimer models on ’quasicrystals’: real materials which can be described mathematically as aperiodic tilings constructed as slices through higher-dimensional crystals. Can dominoes (dimers) be placed on the tiling’s edges such that every vertex connects to one dimer? Or must there be a density of particle-like ’monomer’ defects not connected to dimers? The advantage of working with quasicrystals is that they are random enough to get non-trivial results, but ordered enough that these results can be proven analytically. In previous work [1] we found the minimum density of defects for such models in ’Penrose tilings’, the original quasicrystals discovered by Roger Penrose (recipient of the 2020 Nobel Prize for Physics).

This project has a broad range of possible routes. These include extending to quantum dimer models such as the Rokhsar-Kivelson model (originally introduced to model high-temperature superconductivity, this model features other exotic states of broad current interest such as quantum spin liquids); disorder effects; confinement and the mass gap (including potential relevance to exact solutions in QCD, one of the Clay Institute’s Millennium Prize Problems); related models such as loop-dimer models and Hamiltonian cycles. This project can be taken in a numerical direction (using classical and quantum Monte Carlo techniques), or an analytical direction, seeking exact results. There is scope to work with experimental groups around the world, including in Cardiff, for example implementing similar models in mesoscopic magnetic arrays, or modelling ongoing experiments looking at emergent magnetic monopoles in real materials.

How to Apply:

Applicants should submit an application for postgraduate study via the Cardiff University webpages ( including:

• an upload of your CV
• a personal statement/covering letter
• two references
• Current academic transcripts

Applicants should select Doctor of Philosophy, 3.5 years programme, with a start date of October 2021.

In the research proposal section of your application, please specify the project title and supervisors of this project and copy the project description in the text box provided. In the funding section, please select "I will be applying for a scholarship / grant" and specify that you are applying for advertised funding from EPRSC DTP. Shortlisted candidates will be invited to attend an interview in February/March.

Candidates should hold a good bachelor’s degree (first or upper second-class honours degree) or a MSc degree in Physics or a related subject.

Applicants whose first language is not English will be required to demonstrate proficiency in the English language (IELTS 6.5 or equivalent).

Funding Notes

The studentship includes fees, stipend and RTSG. The stipend and fees are at the UKRI rate (for 2020/21 is £15,285; £4,407 respectively).

There have been recent changes to UKRI eligibility. Studentships are available for Home and International students, with up to 30% of studentships being available for international applicants. Cardiff University is pleased to announce that it will be offering International fee discounts for successful UKRI applicants. The fees will be discounted to the home fees level. Successful applicants will receive a fully-funded studentship and will not be charged the international fee difference.


[1] F. Flicker, S. H. Simon, and S. A. Parameswaran, Classical Dimers on Penrose Tilings, Physical Review X 10, 011005 (2020)

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