In recent years, a highly active area of research has focused on investigating nontrivial topological phases within Non-Hermitian systems. Unlike Hermitian systems, which exhibit real energy spectra, the energy spectra of non-Hermitian Hamiltonian are complex. Among the simplest one-dimensional non-Hermitian systems is the non-reciprocal Su-Schrieffer-Heeger (NSSH) model, which displays three distinct topological phases determined by the real and imaginary energy gap. The classification of these phases relies on a suitable topological invariant known as the complex Zak phase, as described in a recent study [1]. I will briefly discuss the phase boundaries of the non-Hermitian SSH model in the equilibrium setup before addressing the fundamental question: is there any special dynamical characteristic of the non-Hermitian topological phases? To answer that, I will
discuss the quench dynamics between different topological phases of the NSSH model with the help of a well-known quantity, i.e., Loschmidt Echo [2]. I will present how the special phases generated by non-Hermiticity lead to the analyticity in the return rate of the ground state accompanied by the dynamical topological order parameters [3].
references:
[1] Ritu Nehra and Dibyendu Roy, Topology of multipartite non-Hermitian one-dimensional systems, PhysRevB.105.195407, 2022.
[2] Arseni Goussev, Rodolfo A. Jalabert, Horacio M. Pastawski, Diego Wisniacki, Loschmidt Echo, Scholarpedia 7, 11687 , 2012.
[3] Jan Carl Budich and Markus Heyl, Dynamical topological order parameters far from equilibrium, PhysRevB.93.085416, 2016.