Indistinguishable particles in non-Hermitian lattices and their correlations

Quantum random walks of identical particles are ubiquitous in various fields of physics [1]. They give rise to particle number correlations which have been explored in several discrete systems [2; 3]. However, an essential property of all these quantum systems is their Hermiticity. Recently parity-time(PT)-symmetric systems [4] attracted much attention. The Hamiltonians of such systems are not necessarily Hermitian, yet they still can exhibit purely real eigenvalue spectra.