Multiple phase transitions and anomalous non-Hermitian skin effect

Abstract

Non-Hermiticity is revolutionizing the common understanding in the Hermitian scope by interfacing with topological physics. A single non-Hermitian band can host nontrivial topology that is defined over the nonzero windings of the system's eigenvalues, but not the eigenvectors, as opposed to the Hermitian topological systems. This unique non-Hermitian band topology is responsible for the intriguing non-Hermitian skin effect. Here, we show that the band topology of non-Hermitian one-band models can experience multiple phase transitions. Each transition is identified by a change of the eigenvalue winding. Such an interesting phenomenon is enabled by strategically manipulating the long-range couplings. Associated with the multiple phase transitions, the non-Hermitian skin effect exhibits anomalous behaviors, i.e., in different phases, the skin modes take on different forms of wave localizations. At the transition points, the skin modes evolve into Bloch-wavelike extended states, as if the Hermiticity is restored. For demonstration, we consider a modified Hatano-Nelson model with nonreciprocal next-nearest neighbor couplings. Therein, two phase transitions are identified, corresponding to a stationary and a dynamic one (with respect to the reciprocal nearest-neighbor coupling). Exact analytical derivations are performed to analyze the phase transitions and the associated anomalous non-Hermitian skin effect, which show consistency with the numerical results based on the generalized Brillouin zone method. Our work reveals rich non-Hermitian topological physics in one-band systems, which are considered to be topologically trivial in Hermitian systems. By further showing the anomalous non-Hermitian skin effect, intriguing wave manipulations may inspire experiments in classical realms such as photonics and phononics where versatile non-Hermitian controls are feasible.