Quantum dynamics in topological states of matter – DQMT

Advances in material physics and recent progress in experimental techniques has offered ac-cess to novel quantum states of matter together with an unprecedented precision and control in preparation and manipulation of these states. Some of the most exciting examples of these are strongly-correlated topological states of matter, such as quantum spin-liquids and quantum Hall states. These systems raise intriguing theoretical questions and hold the promise of realising new generations of quantum devices, for example from quantum memories or quantum sensors to universal quantum computers. One of the central topics in modern theoretical physics is the far from equilibrium behaviour of interacting many-body systems, which is both of fundamental interest as well as relevant for abovementioned device applications. Non-equilibrium behaviour can be studied, for example, in transport experiments, where one measures the charge current as a function of applied voltage, or the energy current across the sample in the presence of a temperature gradient. Many interesting and surprising observation have been made recently in experiments with quantum Hall edge states, and more recently with quantum-spin liquid candidate materials (most notably RuCl3). In the former setting this allowed, for example, to study the relaxation of non-equilibrium electron distributions due to elec-tron interactions. In these experiments, one can measure electron relaxation by measuring charge currents. However, in topological quantum systems where effective degrees of freedom are chargeless, such as neutral modes expected in certain quantum Hall edge states or Majorana fermions in quantum spin liquids, it is difficult to measure these modes directly with electrical probes. Developing tools for the detection and manipulation of these states is important from a fundamental theoretical perspective as well as for potential applications in quantum computa-tions. In this project, we will study theoretically quantum dynamics and transport phenomena in quantum spin-liquids and quantum Hall systems. Going beyond established results, we will focus on the non-equilibrium behaviour. This work will provide a better understanding of experiments with topological states of matter. Our objective is to extend universal phenomenology of quantum transport and develop new methods for non-equilibrium and thermal transport physics in strong-ly-correlated topological quantum systems.