Phase transitions, criticality and non-trivial topological states in non-equilibrium driven-dissipative systems using analytical methods and tensor ne

The thesis will explore the classification of phase transitions, criticality and non-trivial topological
states in non-equilibrium driven-dissipative quantum systems. In particular, the thesis will focus on
strongly interacting light-matter systems such as exciton-polariton lattices which support rich phenomena
such as high temperature Bose-Einstein condensation, superfluidity and quantum vortices.
The thesis will characterise open driven-dissipative quantum systems by developing analytical techniques,
such as renormalisation group, mean-field theory and Keldysh field theory, and the use of
computational simulations such as tensor network methods, specifically infinite 2D tensor networks
iPEPS.