Unconventional criticality and entanglement from non-Hermiticity

The entanglement entropy encodes fundamental critical scaling properties of quantum many-body systems, and is particularly subtle in non-Hermitian settings where eigenstates generically become non-orthogonal. In this talk, I shall introduce how asymmetric non-Hermitian pumping can lead to exotic entanglement scaling behavior beyond the usual 1/3 log L scaling of gapless free fermion systems. For instance, super volume-law entanglement can result from topological flat bands due to a mechanism dubbed non-Hermitian critical skin compression. Furthermore, competition in the non-Hermitian pumping can give rise to exceptional crossings only at a particular critical system size, leading to non-monotonic dips in the entanglement scaling and unconventional percolation of topological states. Such competition can even emerge from appropriately designed many-body hoppings, leading to curious interaction-induced anomalous scaling behavior. Our discoveries sheds light on a new interplay between topology and entanglement, and have been physically demonstrated on digital quantum processors.