Duality approach to non-equilibrium quantum matter

The systematic understanding of equilibrium collective phenomena through the principles of symmetry and scale is one of the landmark achievements of last century's theoretical physics. The present day analogue is to deduce the laws governing the collective phenomena occurring out of equilibrium, and their basic organising principles, with particular attention to those in complex quantum systems. Solving this problem requires us to overcome the monumental obstacle represented by the lack of general methods to study large interacting quantum systems out of equilibrium. This project tackles this problem from a new perspective based on a “duality” between space and time. The basic idea is that by exchanging the roles of time and one of the spatial coordinates one can turn questions about the non-equilibrium properties of a given system into questions about the stationary properties of a different “dual system”. The price to pay is that the dual system generically undergoes hybrid quantum dynamics involving both unitary evolution and measurements. Nevertheless, this viewpoint allows one to think about non-equilibrium quantum matter through our conventional lenses based on equilibrium physics. The project is structured in two main branches. The first aims at identifying minimal interacting models where the steady state of the dual evolution is exactly accessible, thus yielding new paradigms of solvable many-body dynamics. The second branch aims to go beyond exact solvability. It will provide a classification of the steady states of the space evolution through the lenses of entanglement, link them to the basic features of the evolution, and aid the development of numerical schemes. It will also formulate a perturbative approach to describe non-equilibrium quantum many-body dynamics away from the solvable points. Together, these two branches will lay the foundation for a comprehensive theory of non-equilibrium quantum matter.