Physics Colloquium - Adventures in Non-Hermitian Quantum Matter (with a Touch of Quantum Information Theory)

The discovery and classification of phases of matter is a long-sought goal in quantum many-body physics, with implications ranging from fundamental advances to next-generation technologies. While this challenge has been traditionally addressed for closed systems in or near equilibrium, many current experimental platforms fall outside this paradigm. In this talk, I will focus on many-body systems of non-interacting bosons, whose dynamics are governed by non‑Hermitian generators. These arise naturally if the system is open, described by a quadratic Lindblad master equation; even in the limiting case of Hamiltonian dynamics, however, effective non-Hermiticity may still arise as a sole consequence of bosonic quantum statistics. In spite of their apparent simplicity, these systems engender a remarkably rich physics. For example, I will outline how quantum-critical behavior may arise in a bosonic Hamiltonian due to the closing of a distinctively non-Hermitian Krein gap, even when a many-body ground state does not exist. Likewise, I will discuss how standard finite-size scaling ideas may fail, due to extreme sensitivity to boundary conditions and the emergence of dynamical metastability - whereby the stability properties of the system in the thermodynamic limit sharply differ from those of any finite-size truncation. Finally, I will hint at how topologically mandated edge-localized Majorana-boson modes may emerge in a transient regime of driven-dissipative bosonic dynamics, providing tight analogues to the zero modes characteristic of topological quantum matter. I will emphasize throughout how tools from continuous-variable quantum information - notably, the scaling of entanglement entropy - can help gaining insight into these diverse phenomena.