Phase Transitions in Open Quantum Systems

Developing accurate simulations of quantum mechanical systems unavoidably involves taking into account coupling to the outside world. Such modelling is important for a wide range of physical systems, whose quantum properties are now routinely measured in the lab. These include arrays of superconducting qubits, cold atoms in optical cavities and semiconductor heterostructures. In these systems fascinatingly complex behaviour occurs due to the competition between the many-body coherent effects and dissipative dynamics. This competition leads to the ability to engineer states which are difficult to realise by any other means. There are also regions of parameter space where, by careful tuning, it is possible for there to be sudden, dramatic changes in behaviour for very small changes in the control parameter realising dissipative phase transitions.

In some very specific cases these phase transitions are well understood. These models are usually amenable to mean-field theory and the resulting transitions are very similar to their equilibrium counterparts. Recently, we have shown that this is not always the case and transitions with very different characteristics can arise. In this project we will use state-of-the-art numerical techniques based on matrix product operators and neural networks to examine the kinds of physics which it is possible to realise in more complex lattice models.