Topologically Protected Negative Entanglement Entropy

Entanglement entropy (EE) is pivotal concept in quantum many-body systems, with intriguing interplays with the topological properties of the system. A well-known example is the characterization of the topological order of many-body states through topological entanglement entropy. Recent studies have unveiled that the occurence of exceptional points (EP) in non-Hermitian systems can lead to a negative value for entanglement entropy. In this talk, we will explore two topological non-Hermitian models wherein exceptional points manifest within the energy bands of topological edge states. By studying the entanglement properties via the biorthogonal basis, we numerically obeserved topologically protected, negative entanglement entropy. Intriguingly, the EE exhbits an unusual, negative scaling behavior relative to the system size in the x,y directions, described by: $S~ -L_y^2log L_x$. The Second Renyi entanglement entropy also exhibits a negative trait. This might potentially be measured experimentally by evaluating the expectation value of the SWAP operator on two identical copies, either within optical lattice systems or via Monte Carlo simulations. Our work elucidates a novel relationship between entanglement and the system's topological features, diverging from the topological entanglement entropy characterized by topological order.