Scaling theory for non-Hermitian topological transitions.

Understanding the critical properties is essential for determining the physical behavior of topological systems. In this context, scaling theories based on the curvature function in momentum space, the renormalization group (RG) method, and the universality of critical exponents have proven effective. In this work, we develop a scaling theory for non-Hermitian topological states of matter.

Critical scaling of a two-orbital topological model with extended neighboring couplings.

Extended-range models are the interesting systems, which has been widely used to understand the non-local properties of the fermions at quantum scale. We aim to study the interplay between criticality and extended range couplings under various symmetry constraints. Here, we consider a two orbital Bernevig-Hughes-Zhang model in one dimension with longer (finite neighbor) and long-range (infinite neighbor) couplings.

Unconventional quantum criticality in a non-Hermitian extended Kitaev chain.

We investigate the nature of quantum criticality and topological phase transitions near the critical lines obtained for the extended Kitaev chain with next nearest neighbor hopping parameters and non-Hermitian chemical potential. We surprisingly find multiple gap-less points, the locations of which in the momentum space can change along the critical line unlike the Hermitian counterpart. The interesting simultaneous occurrences of vanishing and sign flipping behavior by real and imaginary components, respectively of the lowest excitation is observed near the topological phase transition.

Mixed state behavior of Hermitian and non-Hermitian topological models with extended couplings.

Geometric phase is an important tool to define the topology of the Hermitian and non-Hermitian systems. Besides, the range of coupling plays an important role in realizing higher topological indices and transition among them. With a motivation to understand the geometric phases for mixed states, we discuss finite temperature analysis of Hermitian and non-Hermitian topological models with extended range of couplings.

Multi-critical topological transition at quantum criticality.

The investigation and characterization of topological quantum phase transition between gapless phases is one of the recent interest of research in topological states of matter. We consider transverse field Ising model with three spin interaction in one dimension and observe a topological transition between gapless phases on one of the critical lines of this model. We study the distinct nature of these gapless phases and show that they belong to different universality classes.