Würzburg ToCoTronics Colloquium

Lately, a lot of attention, both theoretical and experimental, is directed at the non-Hermitian systems, which can be regarded as a natural approximation of open systems. One of the main drivers of this research is the occurence of special degeneracies in the spectrum of non-Hermitian Hamiltonians called Exceptional Points (EPs). At these points, two or more eigenvalues and corresponding eigenvectors overlap rendering the Hamiltonian defective. EPs can be utilized for quantum sensing and for adiabatic state conversion, to name a few applications. Experimental realization of devices based on EPs is complicated by the need to tune the system to the vicinity of an EP. At the same time, the number of independent parameters required for tuning is diminished in the presence of symmetries. In this talk, I consider the systems with Pseudo-Hermitian symmetry, which is closely related to the usually employed PT-symmetry. I characterize separate non-degenerate levels with a Z2 topological index, corresponding to the signs of the pseudometric operator eigenvalues in the absence of Hermiticity-breaking terms. After that I show that the formation of second-order EPs is governed by this topological index: EPs are provided only by pairs of levels with opposite indices. To demonstrate the approach, I consider transverse-field Ising chain with longitudinal staggered gain and loss, which is pseudo-Hermitian with respect to parity. Using the integrability of the model in the absence of Hermiticity-breaking terms, I compute all the topological indices analytically and then use them to analyze the formation of second- and third-order EPs. As a side note, I also consider the ground state quantum Phase transitions in the thermodynamic limit of the model.