Exotic quantum matter with Majorana fermions

Our Universe supports the existence of a set of generally interacting elementary particles e.g. photons, electrons and quarks which have certain properties and behaviour described by physics. Most of current ICT technologies and condensed matter physics are based on the behaviour of electrons in materials. Electrons, like many other elementary particles, carry a purely quantum mechanical property of `spin. Sometimes, aspects of the physics of materials, atomic/molecular systems, and more generally spin-based physical models can be thought of as describing artificial universes with new particles inside them, so called quasi-particles, with very useful quantum properties. We can then forget to an extent the complicated microscopic details involving interactions between an uncountable number of particles, yet gain a deep understanding of the system in terms of weakly or non- interacting quasi-particles alone. These materials can be engineered by us and controlled on the quantum scale to build new quantum technology, and new exotic phases of matter, operating on the level of the quasi-particles. One important such quasi-particle, fundamentally comprising of the collective and highly complicated interacting motion of countless more elementary particles such as atoms or electrons in special `topological systems, is the so called Majorana fermion. Theoretically, predicted by the young Italian physicist Ettore Majorana in the early 20th century, the Majorana has important quantum properties making its physics interesting. While neutrinos could perhaps be Majorana fermions, the nature of neutrinos is not settled, and there is no conclusive evidence for the existence of Majorana fermions as elementary particles. Before about ten years ago Majoranas were not much more than a theoretical curiosity, but now new experimental signatures are starting to catch up with theory. Majoranas can exist as quasi- particles inside certain materials and physical systems. This project focusses on the new physics of interacting Majorana fermion quasi- particles. One particular focus is on Kitaev-type models. These are physical models of interacting quantum spins, which carry importance for promising noise-tolerant quantum information processing and computation applications, and for fundamental understanding of possible phases of matter in the quantum world. Instead of using the language of quantum spin, Kitaev models can be perhaps better understood and described in terms of emergent Majorana quasi-particles. The study of interacting many-particle quantum systems typically requires high-performance computation and advanced numerical methods to elucidate the physical properties. The project combines both numerical and analytical methods.

The main goals of the project were achieved: to develop a new internationally innovative and competitive research programme on interacting Majoranas. Taking a honeycomb lattice of Majoranas, e.g. but not limited to vortices in a topological s-wave Fermi superfluid, in collaboration at Innsbruck we have shown that the strongly-interacting Majorana-Hubbard model on the honeycomb is in fact highly symmetrical, can be integrable in a new quantum integrability class recently discovered at Oxford and Sydney, contains a (topological) quantum spin liquid ground state, and according to our working theory realises a subsystem error correction and stabilizer code with gauge qubits forming a Bacon-Shor code. The integrability joins our newly discovered system to the high-impact family of Kitaev models, which to my knowledge represent the only currently known exactly-solvable 2D topological quantum systems. We have mapped the critical phenomena of the model using Monte Carlo methods. This research programme yields many opportunities for high-impact results.