Extracting small signals from highly oscillating data: the sign problem in Condensed Matter Physics

Swansea University College of Science/Université Grenoble Alpes Fully-funded PhD Scholarship 2016/2017

Monte Carlo techniques allow us to investigate numerically the properties of a wide class of physical systems. Noticeable exceptions to the efficiency and effectiveness of Monte Carlo techniques are numerical studies studies of models affected by the so-called sign problem. In these systems, large cancellations in numerical results take place that severely affect the predictivity of the simulations. Given the depth and breadth of phenomena afflicted by the sign problem (which include, for instance, models for strongly correlated electrons and systems in particle physics such as Quantum Chromodynamics at non-zero baryon density), solving the sign problem will be one of the greatest breakthrough in the field of Monte Carlo studies.

Among other proposals, the recently introduced LLR (Langfeld-Lucini-Rago) algorithm has been shown to deal successfully with the sign problem in special cases such as the SU(3) spin system. The main objective of this Ph.D. project is use the LLR algorithm for studying Condensed Matter systems affected by the sign problem such as the Hubbard model, which describes the phase transition between a conducting phase and an insulating phase. A full solution of the model will provide a step-change in our understanding of important physical systems such as high temperature superconductors, whose discovery led to a Nobel Prize in 1987.

In order to undertake this programme, in addition to subject-specific training (including advanced topics in Monte Carlo simulations and Condensed Matter Physics), the student will learn skills in software development for High Performance Computing (HPC) architectures, on which the project will be heavily based. In the context of the Science DTC at Swansea and complementing its offer, the supervisory team shall develop the field-specific communication skills of the student, by setting up a progressive programme of engagement that gradually steps up from presentations to the team to paper presentations at major international conferences. An active involvement of the student in the write-up of the research and in the submission of papers to refereed journals will also be promoted. Moreover, the student will be encouraged to devise an original approach to the research project and to suggest possible future directions of investigation.

This is a joint doctorate between Swansea University and Université Grenoble Alps. The appointed student is expected to spend half of the eligible candidature period at Swansea and half at Grenoble.

The successful candidate will be expected to commence their studentship in or January 2017.

Candidates must have a First or Upper Second Class Honours MSci or an MSc degree (with Merit), in a relevant discipline. An IELTS score of 6.5 or equivalent is required for non-native English speakers. A working knowledge of the French language would be useful, but not essential.