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Fully Funded EPSRC & STFC PhD Scholarship: Quantum Criticality with U(2N)-Invariant Fermions

Swansea University - Physics

Qualification Type: PhD
Location: Swansea
Funding for: UK Students, EU Students, International Students
Funding amount: £15,285 p.a. (for 2020/21)
Hours: Full Time
Placed On: 26th November 2020
Closes: 31st January 2021

This scholarship is funded by Engineering and Physical Sciences Research Council (EPSRC) and Science and Technology Facilities Council (STFC).

Start date: October 2021


Quantum Field Theory (QFT) has been the lingua franca of particle physics for over 5 decades, yet most insight is based on QFTs describing weakly- interacting particles, e.g. the Standard Model (SM). Much less is known about the inherently less-tractable strongly-interacting theories; these may have an important role beyond the SM, e.g. in a quantum theory of gravity. This project builds on our long-term interest in QFTs of particles moving in two dimensions, a notable application being low-energy electronic excitations in graphene.

Two-dimensional systems with relativistic fermions are a key feature of many important layered systems in condensed matter physics, including the Quantum Hall Effect, cuprate superconductors, spin liquids, topological insulators, and graphene. A complete and rigorous understanding of the underlying quantum field theory is needed, and this project will apply lattice field theory, a state-of-the-art technique developed for particle physics, to the problem.

The simplest lattice models fail to respect an important internal symmetry of the candidate QFT, firmly rooted in the microscopic tight-binding graphene Hamiltonian, based on the unitary group U(2N) with N the number of fermion flavours. However, a formulation known as Domain Wall Fermions (DWF) can accurately capture U(2N) as the separation Ls between two “walls” becomes large. Simulations of the N=1 model reveal a transition, as interaction strength increases, from a conducting phase in which fermions are light, to an insulating phase where they are “gapped”: i.e. a particle mass is dynamically generated. Precisely at the transition is a Quantum Critical Point (QCP), where this mass becomes the only relevant energy scale providing a reference for all other processes. The project goal is to refine and enhance our understanding of the QCP, by exploring large-Ls exploiting the computing resources of both the STFC DiRAC facility and Supercomputing Wales.

The successful applicant will join a diverse, international, interdisciplinary, and world-leading research environment, benefitting from daily interaction within a group of staff and students counting approximately forty researchers, and from the extensive programme of research seminars, journal clubs and training opportunities of the Particle Physics and Cosmology Theory group at Swansea.


Candidates must have a First, Upper Second Class Honours or a Master’s degree with Merit, in a relevant discipline.

For candidates whose first language is not English, we require IELTS 6.5 (with 6.0 in each component) or equivalent. Please visit our website for a list of acceptable English language tests. We prefer candidates to have already met the English Language requirements at the point of application, although this is not a requirement.

In addition to UK students, international and EU students are eligible to apply for these studentships but should note that they may have to pay the difference between the home UKRI fee and the institutional international student fee.

Funding Details

This three-year fully funded scholarship covers UK tuition fees and an annual stipend set at the minimum UKRI level (currently £15,285 per annum for 2020/21 for full-time students, updated each year).

RTSG support of £1,000 per annum is also provided.

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