Making sense of band topology in open quantum systems

There has been a great deal of work in generalising the notion of band topology to the non-equilibrium setting. Much of this effort has focused on non-Hermitian Bloch Hamiltonians that are thought of as describing lattice systems with loss and gain. In the first part of my talk, I will pedagogically explain some central results of this field. I will then argue, however, that the non-Hermitian framework has fundamental difficulties when we consider quantum many-body systems, even those that do not interact. This will motivate the second part of my talk, where I’ll work out to what extent non-Hermitian topology can be rescued into the more general Lindblad description of open quantum systems.