Perspective: Interactions and Nonlinearity in Non-Hermitian Physics

TL;DR

This paper reviews the evolution of non-Hermitian physics from simple models to complex many-body systems, highlighting new phenomena like interaction-induced topological phases, skin effects, and nonlinear collective behaviors.

Contribution

It provides a comprehensive overview of the recent advances in non-Hermitian many-body physics, emphasizing the interplay of interactions, topology, and nonlinear effects.

Findings

Interaction-induced topological phases identified

Many-body skin effects generalized to complex systems

Observation of skin solitons and dissipative phase transitions

Abstract

For decades, Hermiticity was considered an immutable axiom of quantum mechanics, essential for ensuring real energies and unitary evolution. This perspective has shifted radically, driven by the realization that non-Hermitian Hamiltonians provide a powerful effective description of open quantum systems, granting access to unique phenomena such as Exceptional Points and the Non-Hermitian Skin Effect. In this Perspective, we chart the trajectory of this field, moving from its established foundations in single-particle, linear models to the emerging frontier of interacting many-body systems. We first clarify the physical origins of non-Hermitian dynamics, distinguishing between mean-field approximations, conditional "no-click" evolution, and exact Liouvillian dynamics. We then focus on the rich phenomenology arising from the interplay of non-Hermiticity and interactions. We discuss interaction-induced topological phases, the generalization of skin effects to the many-body Hilbert space, and the distinct signatures of dissipative quantum chaos and complexity. Finally, we highlight collective phenomena in nonlinear regimes, including skin solitons and dissipative phase transitions. We also comment on measurement-induced entanglement transitions and their relation to non-Hermitian spectra and topology. By synthesizing these diverse developments, we provide a roadmap for the future of non-Hermitian physics.