###Emergent Fermions in Quantum Spin Liquids
Project ID: 2228bd1022 (You will need this ID for your application)
Research Theme: Physical Sciences
UCL Lead department: London Centre for Nanotechnology (LCN)
Lead Supervisor: Frank Kruger
Project Summary:
Quantum spin liquids (QSLs) are a novel class of materials in which geometric frustration suppresses magnetic order down to absolute zero temperature. The spins in a QSL are subject to strong zero-point quantum fluctuations between an exponentially large number of degenerate classical states, resulting in a highly entangled quantum mechanical ground state. Such densely entangled quantum matter has enormous potential for future quantum technologies. However, our theoretical understanding of this new form of quantum matter is still in its infancy, despite the rapidly growing number of QSL candidate materials.
In gapless QSLs the spins break up (fractionalise) into fermions and gauge fields. This rather abstract concept explains the continuum of excitations seen in neutron scattering experiments. In the context of theory, the idea of fractionalisation has been put on a firm footing by Alexei Kitaev, who constructed a simple QSL model on the honeycomb lattice and demonstrated that it can be solved in terms of fractionalised fermionic degrees of freedom. Although the emergent fermions don’t carry electric charge, they essentially behave as the electrons in graphene with a relativistic Dirac dispersion around Fermi surface points.
There exist materials that are well described by Kitaev’s toy model, but which exhibit additional interactions. These interactions lead to a phase transition from a QSL to a magnetically ordered state.
The aim of this project is to understand the nature of such quantum phase transitions, in the Kitaev model and in related QSLs. You will learn to represent spin models in terms of interacting Dirac fermions and gauge fields. Using methods of quantum field theory, such as renormalisation-group calculations, you will analyse the behaviour near the magnetic ordering transition and compute critical exponents. You will investigate the changes of magnetic excitation spectra across the transition and compare to experiments.